$$ \begin{aligned} 5z+7 &= -5-z&& \text{move the $ \color{blue}{ -z } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]5z+z &= -5-7&& \text{simplify left and right hand side} \\[1 em]6z &= -12&& \text{ divide both sides by $ 6 $ } \\[1 em]z &= -\frac{12}{6}&& \\[1 em]z &= -2&& \\[1 em] \end{aligned} $$
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