Question
$$(x^3+5x-2)(x^2+4) = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (x^3+5x-2)(x^2+4) &= 0&& \text{simplify left side} \\[1 em]x^5+4x^3+5x^3+20x-2x^2-8 &= 0&& \\[1 em]x^5+9x^3-2x^2+20x-8 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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