$$ \begin{aligned} \frac{4}{5}p+\frac{3}{4}-\frac{3}{4}p+\frac{4}{5} &= 0&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20 \cdot \frac{4}{5}p+20\cdot\frac{3}{4}-20\frac{3}{4}p+20\cdot\frac{4}{5} &= 20\cdot0&& \text{cancel out the denominators} \\[1 em]16p+15-15p+16 &= 0&& \text{simplify left side} \\[1 em]p+31 &= 0&& \text{ move the constants to the right } \\[1 em]p &= -31&& \\[1 em]p &= -31&& \\[1 em] \end{aligned} $$

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