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

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

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

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

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

Multiply (-2 + x) * (2x + x2)
(-2(2x + x2) + x(2x + x2)) = 0
((2x * -2 + x2 * -2) + x(2x + x2)) = 0
((-4x + -2x2) + x(2x + x2)) = 0
(-4x + -2x2 + (2x * x + x2 * x)) = 0
(-4x + -2x2 + (2x2 + x3)) = 0

Combine like terms: -2x2 + 2x2 = 0
(-4x + 0 + x3) = 0
(-4x + x3) = 0

Solving
-4x + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + x2) = 0

Factor a difference between two squares.
x((2 + x)(-2 + 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

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

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

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

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