\(x^4+2x^3-2x^2+2x-3=0\)
\(\Leftrightarrow x^4-x^3+3x^3-3x^2+x^2-x+3x-3=0\)
\(\Leftrightarrow x^3\left(x-1\right)+3x^2\left(x-1\right)+x\left(x-1\right)+3\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^3+3x^2+x+3\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[x^2\left(x+3\right)+\left(x+3\right)\right]\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^2+1\right)\left(x+3\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=1\end{matrix}\right.\)
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