`x^4-x^3-5x^2+4x+4=0`
`<=>(x^4-x^3-x^2)-(4x^2-4x-4)=0`
`<=>x^2(x^2-x-1)-4(x^2-x-1)=0`
`<=>(x^2-x-1)(x^2-4)=0`
`<=>`\(\left[ \begin{array}{l}x^2-x-1=0\\x^2-4=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x(x-1)=1\\x^2=4\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}\left[ \begin{array}{l}x=1\\x-1=1⇔x=2\end{array} \right.\\x=±2 \end{array} \right.\)
`=>x={-2;1;2}`