$$ \begin{aligned} \frac{1}{5}c-\frac{5}{6} &= \frac{4}{5}c+\frac{1}{2}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{1}{5}c-30\cdot\frac{5}{6} &= 30 \cdot \frac{4}{5}c+30\cdot\frac{1}{2}&& \text{cancel out the denominators} \\[1 em]6c-25 &= 24c+15&& \text{move the $ \color{blue}{ 24c } $ to the left side and $ \color{blue}{ -25 }$ to the right} \\[1 em]6c-24c &= 15+25&& \text{simplify left and right hand side} \\[1 em]-18c &= 40&& \text{ divide both sides by $ -18 $ } \\[1 em]c &= -\frac{40}{18}&& \\[1 em]c &= -\frac{20}{9}&& \\[1 em] \end{aligned} $$

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