$$ \begin{aligned} -4(x+5) &= \frac{5}{3}(3x-12)&& \text{simplify left and right hand side} \\[1 em]-(4x+20) &= \frac{15x-60}{3}&& \\[1 em]-4x-20 &= \frac{15x-60}{3}&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot-4x-3\cdot20 &= 3 \cdot \frac{15x-60}{3}&& \text{cancel out the denominators} \\[1 em]-12x-60 &= 15x-60&& \text{move the $ \color{blue}{ 15x } $ to the left side and $ \color{blue}{ -60 }$ to the right} \\[1 em]-12x-15x &= -60+60&& \text{simplify left and right hand side} \\[1 em]-27x &= 0&& \text{ divide both sides by $ -27 $ } \\[1 em]x &= \frac{0}{-27}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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