$$ \begin{aligned} 12+\frac{20}{x} &= 10&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot12+x\cdot\frac{20}{x} &= x\cdot10&& \text{cancel out the denominators} \\[1 em]12x+20 &= 10x&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ 20 }$ to the right} \\[1 em]12x-10x &= -20&& \text{simplify left side} \\[1 em]2x &= -20&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= -\frac{20}{2}&& \\[1 em]x &= -10&& \\[1 em] \end{aligned} $$

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