$$ \begin{aligned} 7-8x &= 7\cdot(1+7x)&& \text{simplify left and right hand side} \\[1 em]-8x+7 &= 7+49x&& \\[1 em]-8x+7 &= 49x+7&& \text{move the $ \color{blue}{ 49x } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]-8x-49x &= 7-7&& \text{simplify left and right hand side} \\[1 em]-57x &= 0&& \text{ divide both sides by $ -57 $ } \\[1 em]x &= \frac{0}{-57}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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