Question
$$10x\cdot\frac{5}{12} = 0$$
Answer
$$ x = 0 $$
Explanation
$$ \begin{aligned} 10x\cdot\frac{5}{12} &= 0&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]1210x\cdot\frac{5}{12} &= 12\cdot0&& \text{cancel out the denominators} \\[1 em]50x &= 0&& \text{ divide both sides by $ 50 $ } \\[1 em]x &= \frac{0}{50}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$
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