$$ \begin{aligned} -\frac{5}{2}(3x+4)\cdot6-3x &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]-2 \cdot \frac{5}{2}(3x+4)\cdot6-2\cdot3x &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]-(90x+120)-6x &= 0&& \text{simplify left side} \\[1 em]-90x-120-6x &= 0&& \\[1 em]-96x-120 &= 0&& \text{ move the constants to the right } \\[1 em]-96x &= 120&& \text{ divide both sides by $ -96 $ } \\[1 em]x &= -\frac{120}{96}&& \\[1 em]x &= -\frac{5}{4}&& \\[1 em] \end{aligned} $$

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