$$ \begin{aligned} 12-\frac{4}{5}(x+15) &= \frac{2}{5}x+6&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot12-5 \cdot \frac{4}{5}(x+15) &= 5 \cdot \frac{2}{5}x+5\cdot6&& \text{cancel out the denominators} \\[1 em]60-(4x+60) &= 2x+30&& \text{simplify left side} \\[1 em]60-4x-60 &= 2x+30&& \\[1 em]60-4x-60 &= 2x+30&& \\[1 em]-4x &= 2x+30&& \text{move the $ \color{blue}{ 2x } $ to the left side} \\[1 em]-4x-2x &= 30&& \text{simplify left side} \\[1 em]-6x &= 30&& \text{ divide both sides by $ -6 $ } \\[1 em]x &= -\frac{30}{6}&& \\[1 em]x &= -5&& \\[1 em] \end{aligned} $$

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