$$\frac{1-4x}{2-3x} = 0$$

$$ \begin{aligned} \frac{1-4x}{2-3x} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2-3x }. \\[1 em](2-3x)\frac{1-4x}{2-3x} &= (2-3x)\cdot0&& \text{cancel out the denominators} \\[1 em]1-4x &= 0&& \text{ move the constants to the right } \\[1 em]-4x &= -1&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= \frac{-1}{-4}&& \\[1 em]x &= \frac{1}{4}&& \\[1 em] \end{aligned} $$

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