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

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

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

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

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

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

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

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

Solving
4x + -2x2 = 2

Solving for variable 'x'.

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

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

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

Factor a trinomial.
2((-1 + x)(1 + -1x)) = 0

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

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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 = 0 + 1

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {1, 1}