$$\frac{-x}{x+6} = \frac{2}{5}$$

$$ \begin{aligned} \frac{-x}{x+6} &= \frac{2}{5}&& \text{multiply ALL terms by } \color{blue}{ (x+6)\cdot5 }. \\[1 em](x+6)\cdot5 \cdot \frac{-x}{x+6} &= (x+6)\cdot5\cdot\frac{2}{5}&& \text{cancel out the denominators} \\[1 em]-5x &= 2x+12&& \text{move the $ \color{blue}{ 2x } $ to the left side} \\[1 em]-5x-2x &= 12&& \text{simplify left side} \\[1 em]-7x &= 12&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= -\frac{12}{7}&& \\[1 em] \end{aligned} $$

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