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

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


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

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

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

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

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

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

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

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

Solving
4 + -4x + x2 = 8 + -2x + -1x2

Solving for variable 'x'.

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

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

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

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

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

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

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

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

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

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-1, 2}

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