\(x^4+2x^3-2x^2+2x-3=0\)
\(\left(x^4-1\right)+\left(2x^3-2x^2\right)+\left(2x-2\right)=0\)
\(\left(x-1\right)\left(x+1\right)\left(x^2+1\right)+2x^2\left(x-1\right)+2\left(x-1\right)=0\)
\(\left(x-1\right)\left[\left(x+1\right)\left(x^2+1\right)+2x^2+2\right]=0\)
\(\left(x-1\right)\left(x^3+x+x^2+1+2x^2+2\right)=0\)
\(\left(x-1\right)\left(x^3+3x^2+x+3\right)\)
\(\left(x-1\right)=0or\left(x^3+3x^2+x+3\right)=0\)
\(x-1=0\Leftrightarrow x=1\)\(x^3+3x^2+x+3=0\Leftrightarrow x\left(x^2+1\right)+3\left(x^2+1\right)=0\Leftrightarrow\left(x+3\right)\left(x^2+1\right)=0\Leftrightarrow x+3=0\left(x^2+1>0\right)\Leftrightarrow x=-3\)
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