$$ \begin{aligned} \frac{2}{x+3} &= -7&& \text{multiply ALL terms by } \color{blue}{ x+3 }. \\[1 em](x+3)\cdot\frac{2}{x+3} &= (x+3)\cdot(-7)&& \text{cancel out the denominators} \\[1 em]2 &= -7x-21&& \text{ swap the left and right side of the equation } \\[1 em]-7x-21 &= 2&& \text{ move -21 to the right } \\[1 em]-7x &= 2+21&& \\[1 em]-7x &= 23&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= -\frac{23}{7}&& \\[1 em] \end{aligned} $$

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