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

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


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

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

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

Multiply (-2 + x) * (2 + x)
(-2(2 + x) + x(2 + x)) = 2x + -4
((2 * -2 + x * -2) + x(2 + x)) = 2x + -4
((-4 + -2x) + x(2 + x)) = 2x + -4
(-4 + -2x + (2 * x + x * x)) = 2x + -4
(-4 + -2x + (2x + x2)) = 2x + -4

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

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

Add '4' to each side of the equation.
-4 + 4 + x2 = -4 + 4 + 2x

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

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

Solving
x2 = 2x

Solving for variable 'x'.

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

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

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

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