\(2x^4+x^3-6x^2+x+2=0\)
\(\Leftrightarrow2x^4+x^3+4x^3+2x^2-4x^3-2x^2-8x^2-4x+2x^2+x+4x+2=0\)
\(\Leftrightarrow x^3\left(2x+1\right)+2x^2\left(2x+1\right)-2x^2\left(2x+1\right)-4x\left(2x+1\right)+x\left(2x+1\right)+2\left(2x+1\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(x^3+2x^2-2x^2-4x+x+2\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left[x^2\left(x+2\right)-2x\left(x+2\right)+\left(x+2\right)\right]=0\)
\(\Leftrightarrow\left(2x+1\right)\left(x+2\right)\left(x^2-2x+1\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(x+2\right)\left(x-1\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\frac{1}{2}\\x=-2\\x=1\end{matrix}\right.\)
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