$$\frac{-8q+68}{q-9} = 0$$

$$ \begin{aligned} \frac{-8q+68}{q-9} &= 0&& \text{multiply ALL terms by } \color{blue}{ q-9 }. \\[1 em](q-9)\frac{-8q+68}{q-9} &= (q-9)\cdot0&& \text{cancel out the denominators} \\[1 em]-8q+68 &= 0&& \text{ move the constants to the right } \\[1 em]-8q &= -68&& \text{ divide both sides by $ -8 $ } \\[1 em]q &= \frac{-68}{-8}&& \\[1 em]q &= \frac{17}{2}&& \\[1 em] \end{aligned} $$

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