$$ \begin{aligned} 3z-10 &= z+10+4z&& \text{simplify right side} \\[1 em]3z-10 &= 5z+10&& \text{move the $ \color{blue}{ 5z } $ to the left side and $ \color{blue}{ -10 }$ to the right} \\[1 em]3z-5z &= 10+10&& \text{simplify left and right hand side} \\[1 em]-2z &= 20&& \text{ divide both sides by $ -2 $ } \\[1 em]z &= -\frac{20}{2}&& \\[1 em]z &= -10&& \\[1 em] \end{aligned} $$

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