$$ \begin{aligned} \frac{1}{4}(2x+5) &= \frac{2}{5}(x-2)&& \text{simplify left and right hand side} \\[1 em]\frac{2x+5}{4} &= \frac{2x-4}{5}&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20 \cdot \frac{2x+5}{4} &= 20 \cdot \frac{2x-4}{5}&& \text{cancel out the denominators} \\[1 em]10x+25 &= 8x-16&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ 25 }$ to the right} \\[1 em]10x-8x &= -16-25&& \text{simplify left and right hand side} \\[1 em]2x &= -41&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= -\frac{41}{2}&& \\[1 em] \end{aligned} $$

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