work out

1.  Accomplish by work or effort, as in I think we can work out a solution to this problem. [1500s] For work out all right, see turn out all right.
2.  Find a solution for, solve, as in They hoped to work out their personal differences, or Can you help me work out this equation? [Mid-1800s]
3.  Formulate or develop, as in We were told to work out a new plan, or He's very good at working out complicated plots. [Early 1800s]
4.  Discharge a debt by working instead of paying money, as in She promised she'd work out the rest of the rent by baby-sitting for them. [Second half of 1600s]
5.  Prove effective or successful, as in I wonder if their marriage will work out.
6.  Have a specific result, add up, as in It worked out that she was able to go to the party after all, or The total works out to more than a million. [Late 1800s]
7.  Engage in strenuous exercise for physical conditioning, as in He works out with weights every other day. [1920s]
8.  Exhaust a resource, such as a mine, as in This mine has been completely worked out. [Mid-1500s]

The verb has 8 meanings:

Meaning #1: come up with
  Synonym: work up

Meaning #2: happen in a certain way, leading to, producing, or resulting in a certain outcome, often well

Meaning #3: work out in detail
  Synonym: elaborate

Meaning #4: do physical exercise
  Synonym: exercise

Meaning #5: be calculated

Meaning #6: make a mathematical calculation or computation
  Synonyms: calculate, cipher, cypher, compute, reckon, figure

Meaning #7: find the solution to (a problem or question) or udnerstand the meaning of
  Synonyms: solve, figure out, puzzle out, lick, work

Meaning #8: give a work-out to
  Synonyms: exercise, work