1) 7x^3-63x=0
7x(x^2-9)=0
7x=0 (x^2-9)=0
x=0 (x-3)(x+3)=0
x=0 x=3 x=-3
2) 49x^3-14x^2+x=0
x(49x^2-14x+1)=0
x(7x-1)^2=0
x=0 x=1/7
3) x^3-5x^2-x+5=0
x^2(x-5)-(x-5)=0
(x-5)(x^2-1)=0
x-5=0 x^2-1=0
x=5 x^2=1
x=5 x=-1 x=1
4)x^3-3x^2-4x+12=0
x^2(x-3)-4(x-3)=0
(x-3)(x^2-4)=0
x-3=0 x^2-4=0
x=3 x^2=4
x=3 x=-2 x=2
5) x^4+2x^3+8x+16=0
x(x^3+8)+2(x^3+8)=0
(x^3+8)(x+2)=0
x^3+8=0 x+2=0
x^3=-8 x=2
x=-2 x=2
6) x^5-4x^4+4x^3-x^2+4x-4=0
(x^5-x^2)-(4x^4-4x)+(4x^3-4)=0
x^2(x^3-1)-4x(x^3-1)+4(x^3-1)=0
(x^3-1)(x^2-4x+4)=0
x^3-1=0 x^2-4x+4=0
x^3=1 (x-2)^2=0
x=1 x=2