$$ \begin{aligned} 3+2x\cdot\frac{4}{3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot3+32x\cdot\frac{4}{3} &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]9+8x &= 0&& \text{ move the constants to the right } \\[1 em]8x &= -9&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= -\frac{9}{8}&& \\[1 em] \end{aligned} $$

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