$$ \begin{aligned} 9x-156 &= \frac{3}{2}x+36&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot9x-2\cdot156 &= 2 \cdot \frac{3}{2}x+2\cdot36&& \text{cancel out the denominators} \\[1 em]18x-312 &= 3x+72&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -312 }$ to the right} \\[1 em]18x-3x &= 72+312&& \text{simplify left and right hand side} \\[1 em]15x &= 384&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= \frac{384}{15}&& \\[1 em]x &= \frac{128}{5}&& \\[1 em] \end{aligned} $$

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