x^2=(2x)(x-2)

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


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

Remove parenthesis around (2x)
x2 = 2x(x + -2)

Reorder the terms:
x2 = 2x(-2 + x)
x2 = (-2 * 2x + x * 2x)
x2 = (-4x + 2x2)

Solving
x2 = -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
4x + x2 + -2x2 = -4x + 2x2 + 4x + -2x2

Combine like terms: x2 + -2x2 = -1x2
4x + -1x2 = -4x + 2x2 + 4x + -2x2

Reorder the terms:
4x + -1x2 = -4x + 4x + 2x2 + -2x2

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 4}

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