To solve the given equation \(2(x+15)=-4(5x-2)\) and prove that \(x=-1\), we will follow these steps:
Distribute the constants on both sides of the equation: \[ 2(x + 15) = -4(5x - 2) \] This becomes: \[ 2x + 30 = -20x + 8 \]
Move all terms involving \(x\) to one side and constant terms to the other side: \[ 2x + 20x = 8 - 30 \] Simplifying gives: \[ 22x = -22 \]
Divide both sides by 22 to isolate \(x\): \[ x = \frac{-22}{22} \] Thus, we find: \[ x = -1 \]
The solution to the equation is \(\boxed{x = -1}\).
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