$$ \begin{aligned} 5 \cdot \frac{m+3}{4}\cdot3+2 &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]45 \cdot \frac{m+3}{4}\cdot3+4\cdot2 &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]15m+45+8 &= 0&& \text{simplify left side} \\[1 em]15m+53 &= 0&& \text{ move the constants to the right } \\[1 em]15m &= -53&& \text{ divide both sides by $ 15 $ } \\[1 em]m &= -\frac{53}{15}&& \\[1 em] \end{aligned} $$

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