3x^4-2x^3-9x^2+12x-4=
x^3(3x-2)-(3x-2)^2=
(x^3-3x+2)(3x-2)=
(x^3-1-3x+3)(3x-2)=
[(x-1)(x^2+x+1)-3(x-1)](3x-2)=
[(x-1)(x^2+x-2)](3x-2)=
(x-1)^2(x+2)(3x-2)=0