$$ \begin{aligned} 2a-\frac{1}{2}(a-6) &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot2a-2 \cdot \frac{1}{2}(a-6) &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]4a-(1a-6) &= 0&& \text{simplify left side} \\[1 em]4a-a+6 &= 0&& \\[1 em]3a+6 &= 0&& \text{ move the constants to the right } \\[1 em]3a &= -6&& \text{ divide both sides by $ 3 $ } \\[1 em]a &= -\frac{6}{3}&& \\[1 em]a &= -2&& \\[1 em] \end{aligned} $$

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