Question
$$3x-\frac{3}{2}(2x+8) = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 3x-\frac{3}{2}(2x+8) &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot3x-2 \cdot \frac{3}{2}(2x+8) &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]6x-(6x+24) &= 0&& \text{simplify left side} \\[1 em]6x-6x-24 &= 0&& \\[1 em]6x-6x-24 &= 0&& \\[1 em]-24 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ -24 = 0 } $ is FALSE, we conclude that the equation has no solution.
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