$$x^3+x^2+x+3 = -2$$
Answer
$$ \begin{matrix}x_1 = -1.88124 & x_2 = 0.44062+1.56961i & x_3 = 0.44062-1.56961i \end{matrix} $$
Explanation
$$ \begin{aligned} x^3+x^2+x+3 &= -2&& \text{move all terms to the left hand side } \\[1 em]x^3+x^2+x+3+2 &= 0&& \text{simplify left side} \\[1 em]x^3+x^2+x+5 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Polynomial Equations Solver