Question

(X^2-x)^2-14(x^2-x)+24=0

Answer 1

$(x^2-x)^2-14(x^2-x)+24=0 \\ x^4-2x^3+x^2-14x^2+14x+24=0 \\ x^4-2x^3-13x^2+14x+24=0 \\ x^4-4x^3+2x^3-8x^2-5x^2+20x-6x+24=0 \\ x^3(x-4)+2x^2(x-4)-5x(x-4)-6(x-4)=0 \\ (x^3+2x^2-5x-6)(x-4)=0 \\ (x^3-2x^2+4x^2-8x+3x-6)(x-4)=0 \\ (x^2(x-2)+4x(x-2)+3(x-2))(x-4)=0 \\ (x^2+4x+3)(x-2)(x-4)=0 \\ (x^2+x+3x+3)(x-2)(x-4)=0 \\ (x(x+1)+3(x+1))(x-2)(x-4)=0 \\ (x+3)(x+1)(x-2)(x-4)=0 \\ x+3=0 \ \lor \ x+1=0 \ \lor \ x-2=0 \ \lor \ x-4=0 \\ x=-3 \ \lor \ x=-1 \ \lor \ x=2 \ \lor \ x=4$
$\boxed{x=-3 \hbox{ or } x=-1 \hbox{ or } x=2 \hbox{ or } x=4}$