$$x\cdot2+3x-\frac{4}{6} = 0$$

$$ \begin{aligned} x\cdot2+3x-\frac{4}{6} &= 0&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6x\cdot2+6\cdot3x-6\cdot\frac{4}{6} &= 6\cdot0&& \text{cancel out the denominators} \\[1 em]12x+18x-4 &= 0&& \text{simplify left side} \\[1 em]30x-4 &= 0&& \text{ move the constants to the right } \\[1 em]30x &= 4&& \text{ divide both sides by $ 30 $ } \\[1 em]x &= \frac{4}{30}&& \\[1 em]x &= \frac{2}{15}&& \\[1 em] \end{aligned} $$

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