Question
$$\frac{2}{5}\cdot(18-2^3)+\frac{\frac{12}{1}}{4} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{2}{5}\cdot(18-2^3)+\frac{\frac{12}{1}}{4} &= 0&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20 \cdot \frac{2}{5}\cdot(18-2^3)+20\frac{\frac{12}{1}}{4} &= 20\cdot0&& \text{cancel out the denominators} \\[1 em]80+60 &= 0&& \text{simplify left side} \\[1 em]140 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 140 = 0 } $ is FALSE, we conclude that the equation has no solution.
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