To solve the equation \(-3(2x + 7) = 0\) for \(x\), we will go through the steps one by one.
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Distribute the -3: \[ -3 \cdot 2x + (-3) \cdot 7 = -6x - 21 \] So, the equation becomes: \[ -6x - 21 = 0 \]
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Add 21 to both sides: \[ -6x - 21 + 21 = 0 + 21 \] This simplifies to: \[ -6x = 21 \]
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Divide both sides by -6: \[ x = \frac{21}{-6} \] This can be simplified to: \[ x = -\frac{21}{6} \]
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Simplify the fraction: \[ x = -\frac{7}{2} \]
So the solution to the equation \(-3(2x + 7) = 0\) is: \[ \boxed{-\frac{7}{2}} \]