Solve the quartic equation With $x \in R$. Solve the equation $$x^4+(x-1)(x^2-2x+2)=0$$



Idea 1: $(x^2-x+1)(x^2+2x-2)=0$

Idea 2:$(2x^2+x-1)^2=(3x-3)^2$

Idea 3:$&lt;=&gt;x^4(x-1)x^2-2(x-1)^2=0$

Let $y=x-1$.....

I need another way because I am collecting methods of solving with quartic equations
Some methods of solving the quatric equations are described Here
Some methods of solving the quatric equations are described Here