$$ \begin{aligned} \frac{7}{10}m-\frac{1}{3}m+2m &= 0&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{7}{10}m-30\frac{1}{3}m+30\cdot2m &= 30\cdot0&& \text{cancel out the denominators} \\[1 em]21m-10m+60m &= 0&& \text{simplify left side} \\[1 em]71m &= 0&& \text{ divide both sides by $ 71 $ } \\[1 em]m &= \frac{0}{71}&& \\[1 em]m &= 0&& \\[1 em] \end{aligned} $$

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