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

Solution for (x-2)(2+x)=(x-3)-1 equation:

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

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

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

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

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

Remove parenthesis around (-3 + x)
-4 + x2 = -3 + x + -1

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

Combine like terms: -3 + -1 = -4
-4 + x2 = -4 + x

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

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

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

Solving
x2 = x

Solving for variable 'x'.

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

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

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

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
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 = {0, 1}