$$ \begin{aligned} x+\frac{3}{5} &= -6&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5x+5\cdot\frac{3}{5} &= 5\cdot(-6)&& \text{cancel out the denominators} \\[1 em]5x+3 &= -30&& \text{ move 3 to the right } \\[1 em]5x &= -30-3&& \\[1 em]5x &= -33&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{33}{5}&& \\[1 em] \end{aligned} $$

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