$$ \begin{aligned} \frac{1}{2}x-3x &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{1}{2}x-2\cdot3x &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]x-6x &= 0&& \text{simplify left side} \\[1 em]-5x &= 0&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= \frac{0}{-5}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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