$$ \begin{aligned} 3x+7 &= 2x-6-7(6x+3)&& \text{simplify right side} \\[1 em]3x+7 &= 2x-6-(42x+21)&& \\[1 em]3x+7 &= 2x-6-42x-21&& \\[1 em]3x+7 &= -40x-27&& \text{move the $ \color{blue}{ -40x } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]3x+40x &= -27-7&& \text{simplify left and right hand side} \\[1 em]43x &= -34&& \text{ divide both sides by $ 43 $ } \\[1 em]x &= -\frac{34}{43}&& \\[1 em] \end{aligned} $$

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