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

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

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

Reorder the terms:
-1x(-2 + x) = (x + -2)(x + 2)
(-2 * -1x + x * -1x) = (x + -2)(x + 2)
(2x + -1x2) = (x + -2)(x + 2)

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

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

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

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

Solving
2x + -1x2 = -4 + x2

Solving for variable 'x'.

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

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

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

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

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

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

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
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
Solution
x = {2, -1}