$$ \begin{aligned} \frac{2}{3}\cdot(15+6a) &= 0&& \text{simplify left side} \\[1 em]\frac{12a+30}{3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{12a+30}{3} &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]12a+30 &= 0&& \text{ move the constants to the right } \\[1 em]12a &= -30&& \text{ divide both sides by $ 12 $ } \\[1 em]a &= -\frac{30}{12}&& \\[1 em]a &= -\frac{5}{2}&& \\[1 em] \end{aligned} $$

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