$$ \begin{aligned} \frac{3}{5}a+\frac{1}{6}a &= 0&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{3}{5}a+30\frac{1}{6}a &= 30\cdot0&& \text{cancel out the denominators} \\[1 em]18a+5a &= 0&& \text{simplify left side} \\[1 em]23a &= 0&& \text{ divide both sides by $ 23 $ } \\[1 em]a &= \frac{0}{23}&& \\[1 em]a &= 0&& \\[1 em] \end{aligned} $$

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