$$ \begin{aligned} 12 \cdot \frac{x}{5}+2x &= 0&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot12 \cdot \frac{x}{5}+5\cdot2x &= 5\cdot0&& \text{cancel out the denominators} \\[1 em]12x+10x &= 0&& \text{simplify left side} \\[1 em]22x &= 0&& \text{ divide both sides by $ 22 $ } \\[1 em]x &= \frac{0}{22}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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