x^2=-x^2+4x

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Solution for x^2=-x^2+4x equation: 


Simplifying
x2 = -1x2 + 4x

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

Solving
x2 = 4x + -1x2

Solving for variable 'x'.

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

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

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

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

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

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

Ignore the factor 2.

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
Solution
x = {0, 2}

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