$$ \begin{aligned} \frac{2}{3}(w-5) &= \frac{3}{4}(w+2)&& \text{simplify left and right hand side} \\[1 em]\frac{2w-10}{3} &= \frac{3w+6}{4}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{2w-10}{3} &= 12 \cdot \frac{3w+6}{4}&& \text{cancel out the denominators} \\[1 em]8w-40 &= 9w+18&& \text{move the $ \color{blue}{ 9w } $ to the left side and $ \color{blue}{ -40 }$ to the right} \\[1 em]8w-9w &= 18+40&& \text{simplify left and right hand side} \\[1 em]-w &= 58&& \text{switch signs on both sides} \\[1 em]w &= -58&& \\[1 em] \end{aligned} $$

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