$$ \begin{aligned} \frac{2}{3}(6x-15) &= 4x+2(x-13)&& \text{simplify left and right hand side} \\[1 em]\frac{12x-30}{3} &= 4x+2x-26&& \\[1 em]\frac{12x-30}{3} &= 6x-26&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{12x-30}{3} &= 3\cdot6x-3\cdot26&& \text{cancel out the denominators} \\[1 em]12x-30 &= 18x-78&& \text{move the $ \color{blue}{ 18x } $ to the left side and $ \color{blue}{ -30 }$ to the right} \\[1 em]12x-18x &= -78+30&& \text{simplify left and right hand side} \\[1 em]-6x &= -48&& \text{ divide both sides by $ -6 $ } \\[1 em]x &= \frac{-48}{-6}&& \\[1 em]x &= 8&& \\[1 em] \end{aligned} $$

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