$$x^4+2x^3+3x^2+4x = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -1.65063 & x_3 = -0.17469+1.54687i \\[1 em] x_4 = -0.17469-1.54687i & \\[1 em] \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ x^{4}+2x^{3}+3x^{2}+4x = 0 } $, first we need to factor our $ x $.
$$ x^{4}+2x^{3}+3x^{2}+4x = x \left( x^{3}+2x^{2}+3x+4 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ x^{3}+2x^{2}+3x+4 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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