Question
$$(3x-1)(x+2)+(x-3)(x^2+3x+9) = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (3x-1)(x+2)+(x-3)(x^2+3x+9) &= 0&& \text{simplify left side} \\[1 em]3x^2+6x-x-2+x^3+3x^2+9x-3x^2-9x-27 &= 0&& \\[1 em]3x^2+5x-2+x^3-27 &= 0&& \\[1 em]x^3+3x^2+5x-29 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Equations Solver