Question
$$(2-3x)(4+6x+9x^2)+27x^3 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (2-3x)(4+6x+9x^2)+27x^3 &= 0&& \text{simplify left side} \\[1 em]8+12x+18x^2-12x-18x^2-27x^3+27x^3 &= 0&& \\[1 em]8+12x+18x^2-12x-18x^2-27x^3+27x^3 &= 0&& \\[1 em]8 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 8 = 0 } $ is FALSE, we conclude that the equation has no solution.
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