Question
$$x^3+3(x+1)^2+10 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^3+3(x+1)^2+10 &= 0&& \text{simplify left side} \\[1 em]x^3+3(x^2+2x+1)+10 &= 0&& \\[1 em]x^3+3x^2+6x+3+10 &= 0&& \text{simplify left side} \\[1 em]x^3+3x^2+6x+13 &= 0&& \\[1 em] \end{aligned} $$
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