To solve the equation \(4(3x + 2) = 32\), follow these steps:
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Distribute the 4 on the left side of the equation: \[ 4 \cdot 3x + 4 \cdot 2 = 32 \implies 12x + 8 = 32 \]
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Subtract 8 from both sides to isolate the term with \(x\): \[ 12x + 8 - 8 = 32 - 8 \implies 12x = 24 \]
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Divide both sides by 12 to solve for \(x\): \[ x = \frac{24}{12} \implies x = 2 \]
Therefore, the solution is: \[ \boxed{2} \]