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

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