Rome fought three wars against Carthage, the Three Punic War. Each war had different reasons.
The First Punic War developed into a contest over the control of Sicily after the Romans intervened in eastern Sicily to help some mercenaries who has seized a city there. They also defeated Syracuse, the most powerful of the Greek city states in eastern and southern Sicily, and forced her to become a Roman ally. This worried the Carthaginians who had possessions in western Sicily and who mobilised for war.
In the Second Punic War, Hannibal, a military commander and the ruler of the Carthaginian possessions in southern Spain, invaded Italy. He wasted to take Rome as a revenge for the first war.
Rome fought the Third Punic War to destroy Carthage.
Rome had fought three wars with Carthage over dominance of the Western Mediterranean. Carthage was so resilient that it kept bouncing back, so Rome went for the 'final solution', selling the people into slavery, and converting Carthage into a resettlement colony for its retired veterans.
They probably mean that when the Romans gained control of central and southern Italy, Rome and Carthage were destined to clash over the control of next door Sicily. The Carthaginians, who had possessions in western Sicily, mobilised for war in against Rome when she intervened militarily to support some mercenaries who had seized the city of Messana, in north-eastern Sicily, on the straight which separates the island from the mainland. These mercenaries had been attacked by Syracuse, the most powerful of the Greek city-states in eastern and southern Sicily. The Romans defeated Syracuse and forced her to become a Roman ally. The Carthaginians were worried about the security of their possessions in the west in the face of this combined power. There had been a friendly relationship between Rome and Carthage which signed three trade treaties. This broke down during the war against Pyrrhus, a Greek King who tried to invade southern Italy by fighting against Rome and, when he failed, went to Sicily and fought against the Carthaginians. The two sides had signed a treaty in which they were meant to help each other against Pyrrhus. Initially Carthage's fleet patrolled the sea between Sicily and Rome to keep an eye on Pyrrhus' fleet, which never reached this sea. When Pyrrhus went to Sicily Rome did not give ant help. The Carthaginians, in their turn, where happy when Pyrrhus left Sicily, returned to the mainland and fought the Romans again. He lost and left Italy, saying "What a battlefield I am leaving for Carthage and Rome!" After this war Rome took over Apulia the heel of Italy, and Calabria the toe of the peninsula, just two miles from Sicily. Carthage and Rome were now the superpowers of the western Mediterranean.
Rome defeated Carthage after three wars and to terminate it, sold its people into slavery and established a colony of retired Roman soldiers on the site. It became dominant in the Western Mediterranean. Rome had also turned on Macedonia to punish it for assisting Carthage in the second war, so beginning its expansion into Eastern Europe.
Rome? After Hannibal retreated back to Carthage (present day Tunisia), the Romans followed him there and wiped out their army. Carthage was basically a commerce state and didn't have much of their own military, just mercenaries. They didn't support Hannibal or the war very well and in the end were overrun. I think Scipio Africanus was instrumental in defeating Carthage, he was a Roman general. - Hannibal wasn't "kicked out of Italy" , he pretty much destroyed all the Roman forces he met, even when he was outnumbered and with no reinforcements. - When Romans couldn't beat him, they decided to attack Carthage the city instead, he was miles from conquering Rome. - Facing that danger Carthage senates recalled Hannibal and ordered him to defend the city, he faced Romans in Battle of Zama which he lost vs Scipio Africanus, mainly because Romans had the Numidians (nowadays Algerians) on their side, Numdians were that era's best Cavalry, they destroyed Carthaginian Cavalry then went to attack Carthage's main force from the back.
Rome and Carthage fought each other three times in three Punic Wars. The causes of each war were different. The First Punic War was precipitated by the Mamertines, southern Italian mercenaries who had seized the city of Messana, on Sicily's east coast and had been attacked by the Greek city of Syracuse, (also on the east coast) the most powerful city in the island. The Mamertines asked both Carthage (which had five ports on the western coast) and Rome for help. Carthage helped first, but established a garrison in the city. The Mamertines were not happy with this and asked Rome for help again. The Roman senate was reluctant to get involved., but the popular assembly voted for war. Rome evicted the Carthaginian garrison in Messana and besieged Syracuse, which became Rome's ally. At this point Carthage mobilised for war. Ancient historian Polybius said that there were concerns in Rome that Carthage's presence in Messana might lead to a clash with Syracuse. If Carthage defeated Syracuse she would take over the whole of Sicily. The Carthaginians, in their turn, were concerned about Rome's alliance with Syracuse. Regarding the Second Punic War, Polybius said that Hannibal wanted this war in revenge for Rome fraudulently seizing Corsica and Sardinia from Carthage by taking advantage of a military rebellion in Carthage after the first war. Cities on the northern part of the coast of Spain allied with Rome for protection because they felt threatened by Carthaginian expansion along that coast. Rome negotiated a treaty that set the river Ebro as the boundary between the two areas. Hannibal broke the treaty by seizing a city just north of this river. Rome tried to negotiate, but these failed. Rome was forced to declare war. Hannibal had already made preparations for a military expedition to Italy and set off very quickly. Hannibal's provocation and the speed of his mobilisation indicate that he did want war. In the Third Punic War Rome wanted to destroy Carthage because the latter had recovered in economic prosperity and because she raised an army to defend herself from territorial encroachments by her Numidian neighbours. Under the term of the peace treaty Carthage was not allowed to raise an army without Rome's permission. The war faction in Rome used this to push for a declaration of war. This faction did not want an economically and possibly militarily resurgent Carthage and wanted to eliminate this foe.
The three Punic Wars went on over 120 years. Rome had many leaders over that period.
Having decisively defeated Carthage , Rome went on to dominate the Mediterranean and expanded the Empire .
Hannibal did not go directly to Rome from Carthage, which was in Tunisia. He went via Spain, and crossed the Alps to get to Italy.
Rome and its allies defeated Carthage. After the Second war, Rome imposed an annual financial penalty designed to cripple Carthage for 50 years. The resilient Carthaginians paid it off in ten years. So after defeating Carthage in the Third Punic War, Rome went for a 'Final Solution' selling the Carthaginians into slavery to get rid of their contest for superiority in the Western Mediterranean.
Rome had fought three wars with Carthage over dominance of the Western Mediterranean. Carthage was so resilient that it kept bouncing back, so Rome went for the 'final solution', selling the people into slavery, and converting Carthage into a resettlement colony for its retired veterans.
Rome, which exterminated its rival in the Western Mediterranean, Carthage, and went on to dominate the Eastern Mediterranean.
Hannibal left from Croto (modern Crotone) in Calabria, the toe of Italy.
The legend does not have Aeneas founding Rome - that was Romulus and Remus. Supposedly after deserting Troy after its capture by the Archeans, Aeneas went via Carthage to central Italy and there in Latinum became the ancestor of Romulus and Remus, but did not found Rome.
Many soldiers of Rome and her allies in Italy lost their farms and migrated to the city of Rome to eke out a living. They lost their farms because prolonged military service led to their neglect or because they had been ravaged during the war. Rich landowners took advantage of their destitution to buy their lands cheaply. Most of Carthage's solders were not from Carthage (which was in Tunisia). They were from Spain, northern Italy and Libya. After the war they went back to their lands. Algerian cavalrymen who had been Carthage's allies and had fought with her switched their alliance to Rome.
They probably mean that when the Romans gained control of central and southern Italy, Rome and Carthage were destined to clash over the control of next door Sicily. The Carthaginians, who had possessions in western Sicily, mobilised for war in against Rome when she intervened militarily to support some mercenaries who had seized the city of Messana, in north-eastern Sicily, on the straight which separates the island from the mainland. These mercenaries had been attacked by Syracuse, the most powerful of the Greek city-states in eastern and southern Sicily. The Romans defeated Syracuse and forced her to become a Roman ally. The Carthaginians were worried about the security of their possessions in the west in the face of this combined power. There had been a friendly relationship between Rome and Carthage which signed three trade treaties. This broke down during the war against Pyrrhus, a Greek King who tried to invade southern Italy by fighting against Rome and, when he failed, went to Sicily and fought against the Carthaginians. The two sides had signed a treaty in which they were meant to help each other against Pyrrhus. Initially Carthage's fleet patrolled the sea between Sicily and Rome to keep an eye on Pyrrhus' fleet, which never reached this sea. When Pyrrhus went to Sicily Rome did not give ant help. The Carthaginians, in their turn, where happy when Pyrrhus left Sicily, returned to the mainland and fought the Romans again. He lost and left Italy, saying "What a battlefield I am leaving for Carthage and Rome!" After this war Rome took over Apulia the heel of Italy, and Calabria the toe of the peninsula, just two miles from Sicily. Carthage and Rome were now the superpowers of the western Mediterranean.
Dumb
The result of the First Punic War was that Rome took over the Carthaginian territory in western Sicily and gained control of the island, which also involved Syracuse, the most powerful Greek state in Sicily, being forced to become an ally of Rome. The Romans also took advantage of a rebellion by the Carthaginian mercenaries to seize Sardinia and Corsica, which were Carthaginian territories. The result of the Second Punic War was that the Romans took over the Carthaginian territories in southern Spain. Moreover, the Numidians (next doors neighbours of Carthage, in Algeria) who had been allies of Carthage switched sides and went over to the Romans. Rome fought the Third Punic War because she wanted to destroy Carthage. The result was that Rome destroyed Carthage and took over her home territory, Tunisia and western Libya. The overall result of these wars is that Rome got rid of her main rival and gained control of the western basin of the Mediterranean.