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To solve the equation ( ab + 3c^2d = 0 ) for ( b ), first isolate the term involving ( b ) by subtracting ( 3c^2d ) from both sides, resulting in ( ab = -3c^2d ). Then, divide both sides by ( a ) (assuming ( a \neq 0 )) to get ( b = \frac{-3c^2d}{a} ).

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