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

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

Simplifying
(x2 + -1x)(x + 2) = 0

Reorder the terms:
(-1x + x2)(x + 2) = 0

Reorder the terms:
(-1x + x2)(2 + x) = 0

Multiply (-1x + x2) * (2 + x)
(-1x * (2 + x) + x2(2 + x)) = 0
((2 * -1x + x * -1x) + x2(2 + x)) = 0
((-2x + -1x2) + x2(2 + x)) = 0
(-2x + -1x2 + (2 * x2 + x * x2)) = 0
(-2x + -1x2 + (2x2 + x3)) = 0

Combine like terms: -1x2 + 2x2 = 1x2
(-2x + 1x2 + x3) = 0

Solving
-2x + 1x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + x + x2) = 0

Factor a trinomial.
x((-2 + -1x)(1 + -1x)) = 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 '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, -2, 1}