$$ \begin{aligned} -\frac{1}{6}x(-\frac{3}{4}) &= 0&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]-12 \cdot \frac{1}{6}x(-\frac{3}{4}) &= 12\cdot0&& \text{cancel out the denominators} \\[1 em]-\frac{-3}{2}x &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]-2 \cdot \frac{-3}{2}x &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]--3x &= 0&& \text{simplify left side} \\[1 em]3x &= 0&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{0}{3}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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