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

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


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

Reorder the terms:
x2(-2 + x) + x(x + -2) = 0
(-2 * x2 + x * x2) + x(x + -2) = 0
(-2x2 + x3) + x(x + -2) = 0

Reorder the terms:
-2x2 + x3 + x(-2 + x) = 0
-2x2 + x3 + (-2 * x + x * x) = 0
-2x2 + x3 + (-2x + x2) = 0

Reorder the terms:
-2x + -2x2 + x2 + x3 = 0

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

Solving
-2x + -1x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + -1x + x2) = 0

Factor a trinomial.
x((-1 + -1x)(2 + -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 '(-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

Subproblem 3
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
Solution
x = {0, -1, 2}

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