(2-x)(x(x-2))=0

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


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

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

Multiply (2 + -1x) * (-2x + x2)
(2(-2x + x2) + -1x * (-2x + x2)) = 0
((-2x * 2 + x2 * 2) + -1x * (-2x + x2)) = 0
((-4x + 2x2) + -1x * (-2x + x2)) = 0
(-4x + 2x2 + (-2x * -1x + x2 * -1x)) = 0
(-4x + 2x2 + (2x2 + -1x3)) = 0

Combine like terms: 2x2 + 2x2 = 4x2
(-4x + 4x2 + -1x3) = 0

Solving
-4x + 4x2 + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + 4x + -1x2) = 0

Factor a trinomial.
x((-2 + x)(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 '(-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 + -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, 2, 2}

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