$$ \begin{aligned} 8x+\frac{12}{5} &= 0&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot8x+5\cdot\frac{12}{5} &= 5\cdot0&& \text{cancel out the denominators} \\[1 em]40x+12 &= 0&& \text{ move the constants to the right } \\[1 em]40x &= -12&& \text{ divide both sides by $ 40 $ } \\[1 em]x &= -\frac{12}{40}&& \\[1 em]x &= -\frac{3}{10}&& \\[1 em] \end{aligned} $$

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