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

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


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

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

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

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

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

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

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

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

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

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

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

Solving
-4x + x2 = 2x

Solving for variable 'x'.

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

Combine like terms: -4x + -2x = -6x
-6x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-6x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + 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 '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Solution
x = {0, 6}

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