x^2=2x+x(2x-4)+0

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Solution for x^2=2x+x(2x-4)+0 equation: 


Simplifying
x2 = 2x + x(2x + -4) + 0

Reorder the terms:
x2 = 2x + x(-4 + 2x) + 0
x2 = 2x + (-4 * x + 2x * x) + 0
x2 = 2x + (-4x + 2x2) + 0

Reorder the terms:
x2 = 0 + 2x + -4x + 2x2
Remove the zero:
x2 = 2x + -4x + 2x2

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

Solving
x2 = -2x + 2x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
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 + -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}

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