$$ \begin{aligned} \frac{12}{5}x+8 &= 0&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{12}{5}x+5\cdot8 &= 5\cdot0&& \text{cancel out the denominators} \\[1 em]12x+40 &= 0&& \text{ move the constants to the right } \\[1 em]12x &= -40&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= -\frac{40}{12}&& \\[1 em]x &= -\frac{10}{3}&& \\[1 em] \end{aligned} $$

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