$$\frac{4x-5}{2x+7} = \frac{2}{5}$$

$$ \begin{aligned} \frac{4x-5}{2x+7} &= \frac{2}{5}&& \text{multiply ALL terms by } \color{blue}{ (2x+7)\cdot5 }. \\[1 em](2x+7)\cdot5 \cdot \frac{4x-5}{2x+7} &= (2x+7)\cdot5\cdot\frac{2}{5}&& \text{cancel out the denominators} \\[1 em]20x-25 &= 4x+14&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -25 }$ to the right} \\[1 em]20x-4x &= 14+25&& \text{simplify left and right hand side} \\[1 em]16x &= 39&& \text{ divide both sides by $ 16 $ } \\[1 em]x &= \frac{39}{16}&& \\[1 em] \end{aligned} $$

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