(2x-4)-[(x+2)(x-4)]=x^2-4

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

Simplifying
(2x + -4) + -1[(x + 2)(x + -4)] = x2 + -4

Reorder the terms:
(-4 + 2x) + -1[(x + 2)(x + -4)] = x2 + -4

Remove parenthesis around (-4 + 2x)
-4 + 2x + -1[(x + 2)(x + -4)] = x2 + -4

Reorder the terms:
-4 + 2x + -1[(2 + x)(x + -4)] = x2 + -4

Reorder the terms:
-4 + 2x + -1[(2 + x)(-4 + x)] = x2 + -4

Multiply (2 + x) * (-4 + x)
-4 + 2x + -1[(2(-4 + x) + x(-4 + x))] = x2 + -4
-4 + 2x + -1[((-4 * 2 + x * 2) + x(-4 + x))] = x2 + -4
-4 + 2x + -1[((-8 + 2x) + x(-4 + x))] = x2 + -4
-4 + 2x + -1[(-8 + 2x + (-4 * x + x * x))] = x2 + -4
-4 + 2x + -1[(-8 + 2x + (-4x + x2))] = x2 + -4

Combine like terms: 2x + -4x = -2x
-4 + 2x + -1[(-8 + -2x + x2)] = x2 + -4
-4 + 2x + [-8 * -1 + -2x * -1 + x2 * -1] = x2 + -4
-4 + 2x + [8 + 2x + -1x2] = x2 + -4

Reorder the terms:
-4 + 8 + 2x + 2x + -1x2 = x2 + -4

Combine like terms: -4 + 8 = 4
4 + 2x + 2x + -1x2 = x2 + -4

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

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

Solving
4 + 4x + -1x2 = -4 + x2

Solving for variable 'x'.

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

Combine like terms: 4 + 4 = 8
8 + 4x + -1x2 + -1x2 = -4 + x2 + 4 + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
8 + 4x + -2x2 = -4 + x2 + 4 + -1x2

Reorder the terms:
8 + 4x + -2x2 = -4 + 4 + x2 + -1x2

Combine like terms: -4 + 4 = 0
8 + 4x + -2x2 = 0 + x2 + -1x2
8 + 4x + -2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 2x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
4 + 2x + -1x2 = 0

Solving
4 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + -2x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2x + 4 + x2 = 0 + 4

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

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

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

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 4 + 1

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

Combine like terms: 4 + 1 = 5
1 + -2x + x2 = 5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
x + -1 = 2.236067978

Simplifying
x + -1 = 2.236067978

Reorder the terms:
-1 + x = 2.236067978

Solving
-1 + x = 2.236067978

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.236067978 + 1
x = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
x = 3.236067978

Simplifying
x = 3.236067978

Subproblem 2
x + -1 = -2.236067978

Simplifying
x + -1 = -2.236067978

Reorder the terms:
-1 + x = -2.236067978

Solving
-1 + x = -2.236067978

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.236067978 + 1
x = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
x = -1.236067978

Simplifying
x = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.236067978, -1.236067978}
Solution
x = {3.236067978, -1.236067978}