$$ \begin{aligned} \frac{5}{9}(x-32)-45 &= 0&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9 \cdot \frac{5}{9}(x-32)-9\cdot45 &= 9\cdot0&& \text{cancel out the denominators} \\[1 em]5x-160-405 &= 0&& \text{simplify left side} \\[1 em]5x-565 &= 0&& \text{ move the constants to the right } \\[1 em]5x &= 565&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{565}{5}&& \\[1 em]x &= 113&& \\[1 em] \end{aligned} $$

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