$$\frac{g}{g+5} = \frac{g-2}{g+4}$$

$$ \begin{aligned} \frac{g}{g+5} &= \frac{g-2}{g+4}&& \text{multiply ALL terms by } \color{blue}{ (g+5)(g+4) }. \\[1 em](g+5)(g+4)\frac{g}{g+5} &= (g+5)(g+4)\frac{g-2}{g+4}&& \text{cancel out the denominators} \\[1 em]g^2+4g &= g^2+3g-10&& \text{move all terms to the left hand side } \\[1 em]g^2+4g-g^2-3g+10 &= 0&& \text{simplify left side} \\[1 em]g^2+4g-g^2-3g+10 &= 0&& \\[1 em]g+10 &= 0&& \text{ move the constants to the right } \\[1 em]g &= -10&& \\[1 em]g &= -10&& \\[1 em] \end{aligned} $$

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