$$ \begin{aligned} \frac{5}{6}x-\frac{2}{3}-\frac{16}{5}x\cdot\frac{3}{4}+\frac{3}{2}x-\frac{3}{9} &= 0&& \text{multiply ALL terms by } \color{blue}{ 180 }. \\[1 em]180 \cdot \frac{5}{6}x-180\cdot\frac{2}{3}-180\frac{16}{5}x\cdot\frac{3}{4}+180\frac{3}{2}x-180\cdot\frac{3}{9} &= 180\cdot0&& \text{cancel out the denominators} \\[1 em]150x-120-432x+270x-60 &= 0&& \text{simplify left side} \\[1 em]-12x-180 &= 0&& \text{ move the constants to the right } \\[1 em]-12x &= 180&& \text{ divide both sides by $ -12 $ } \\[1 em]x &= -\frac{180}{12}&& \\[1 em]x &= -15&& \\[1 em] \end{aligned} $$

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