$$ \begin{aligned} \frac{2}{5}+p &= \frac{4}{5}+\frac{3}{5}p&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot\frac{2}{5}+5p &= 5\cdot\frac{4}{5}+5\frac{3}{5}p&& \text{cancel out the denominators} \\[1 em]2+5p &= 4+3p&& \text{move the $ \color{blue}{ 3p } $ to the left side and $ \color{blue}{ 2 }$ to the right} \\[1 em]5p-3p &= 4-2&& \text{simplify left and right hand side} \\[1 em]2p &= 2&& \text{ divide both sides by $ 2 $ } \\[1 em]p &= \frac{2}{2}&& \\[1 em]p &= 1&& \\[1 em] \end{aligned} $$

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