$$ \begin{aligned} \frac{3}{5}(2x-10) &= \frac{2}{3}x+10&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15 \cdot \frac{3}{5}(2x-10) &= 15 \cdot \frac{2}{3}x+15\cdot10&& \text{cancel out the denominators} \\[1 em]18x-90 &= 10x+150&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ -90 }$ to the right} \\[1 em]18x-10x &= 150+90&& \text{simplify left and right hand side} \\[1 em]8x &= 240&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= \frac{240}{8}&& \\[1 em]x &= 30&& \\[1 em] \end{aligned} $$

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