x^{3}=x
Solve for zero to get
x^{3 }- x = 0
factor out an x to get
x(x^{2 }- 1) = 0
Now factor what is in the parenthesis by using the difference of squares rule:
so
x(x - 1)(x +1) = 0
now solve for all three answers (separate the factors and set them ALL = 0)
x = 0 , x - 1 = 0 , x + 1 = 0
when you solve these three you get x = 0, x = 1, and x = -1
Bill Fanning
El Paso, TX