x(x^2-1)-x^3+x^2=0

Solution for x(x^2-1)-x^3+x^2=0 equation:

Simplifying
x(x2 + -1) + -1x3 + x2 = 0

Reorder the terms:
x(-1 + x2) + -1x3 + x2 = 0
(-1 * x + x2 * x) + -1x3 + x2 = 0
(-1x + x3) + -1x3 + x2 = 0

Reorder the terms:
-1x + x2 + x3 + -1x3 = 0

Combine like terms: x3 + -1x3 = 0
-1x + x2 + 0 = 0
-1x + x2 = 0

Solving
-1x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1
Solution
x = {0, 1}