(2-x)(2+x)-(2-x)(x+3)=x(2-x)

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Solution for (2-x)(2+x)-(2-x)(x+3)=x(2-x) equation: 


Simplifying
(2 + -1x)(2 + x) + -1(2 + -1x)(x + 3) = x(2 + -1x)

Multiply (2 + -1x) * (2 + x)
(2(2 + x) + -1x * (2 + x)) + -1(2 + -1x)(x + 3) = x(2 + -1x)
((2 * 2 + x * 2) + -1x * (2 + x)) + -1(2 + -1x)(x + 3) = x(2 + -1x)
((4 + 2x) + -1x * (2 + x)) + -1(2 + -1x)(x + 3) = x(2 + -1x)
(4 + 2x + (2 * -1x + x * -1x)) + -1(2 + -1x)(x + 3) = x(2 + -1x)
(4 + 2x + (-2x + -1x2)) + -1(2 + -1x)(x + 3) = x(2 + -1x)

Combine like terms: 2x + -2x = 0
(4 + 0 + -1x2) + -1(2 + -1x)(x + 3) = x(2 + -1x)
(4 + -1x2) + -1(2 + -1x)(x + 3) = x(2 + -1x)

Reorder the terms:
4 + -1x2 + -1(2 + -1x)(3 + x) = x(2 + -1x)

Multiply (2 + -1x) * (3 + x)
4 + -1x2 + -1(2(3 + x) + -1x * (3 + x)) = x(2 + -1x)
4 + -1x2 + -1((3 * 2 + x * 2) + -1x * (3 + x)) = x(2 + -1x)
4 + -1x2 + -1((6 + 2x) + -1x * (3 + x)) = x(2 + -1x)
4 + -1x2 + -1(6 + 2x + (3 * -1x + x * -1x)) = x(2 + -1x)
4 + -1x2 + -1(6 + 2x + (-3x + -1x2)) = x(2 + -1x)

Combine like terms: 2x + -3x = -1x
4 + -1x2 + -1(6 + -1x + -1x2) = x(2 + -1x)
4 + -1x2 + (6 * -1 + -1x * -1 + -1x2 * -1) = x(2 + -1x)
4 + -1x2 + (-6 + 1x + 1x2) = x(2 + -1x)

Reorder the terms:
4 + -6 + 1x + -1x2 + 1x2 = x(2 + -1x)

Combine like terms: 4 + -6 = -2
-2 + 1x + -1x2 + 1x2 = x(2 + -1x)

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

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

Solving for variable 'x'.

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

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

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

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

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


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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