$$ \begin{aligned} -6x+10 &= \frac{2}{5}x+\frac{5}{6}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]-30\cdot6x+30\cdot10 &= 30 \cdot \frac{2}{5}x+30\cdot\frac{5}{6}&& \text{cancel out the denominators} \\[1 em]-180x+300 &= 12x+25&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ 300 }$ to the right} \\[1 em]-180x-12x &= 25-300&& \text{simplify left and right hand side} \\[1 em]-192x &= -275&& \text{ divide both sides by $ -192 $ } \\[1 em]x &= \frac{-275}{-192}&& \\[1 em]x &= \frac{275}{192}&& \\[1 em] \end{aligned} $$

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