$$ \begin{aligned} \frac{12}{3}+3x\cdot3 &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot\frac{12}{3}+33x\cdot3 &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]12+27x &= 0&& \text{ move the constants to the right } \\[1 em]27x &= -12&& \text{ divide both sides by $ 27 $ } \\[1 em]x &= -\frac{12}{27}&& \\[1 em]x &= -\frac{4}{9}&& \\[1 em] \end{aligned} $$

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