<s>[INST] Find roots of $x^4 -6x^3 + 12x^2 - 12 x + 4 = 0$ the original equation is:
$$(x^2 + 2)^2 -6x(x^2+2) + 8x^2=0.$$
cannot see how to go solving this. I tried following way to factorise:
$$(x^2+2)(x^2-6x+2) + 8x^2 = 0.$$
But this has no help to solve. 
Thank you people, but I need the thinking process, not the answer.
 [/INST] One way to find the factorizations others have given is to complete the square.  If you recognize $y^2-6y+9=(y-3)^2$ you can do $(x^2+2)^2-6(x^2+2)+8x^2=((x^2+2)-3x)^2-x^2=(x^2+2-4x)(x^2+2-2x)$
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