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

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

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

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

Remove parenthesis around (2 + x)
2 + x = (x + -3)(x + 2)

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

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

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

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

Solving
2 + x = -6 + -1x + x2

Solving for variable 'x'.

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

Combine like terms: 2 + 6 = 8
8 + x + x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Combine like terms: x + x = 2x
8 + 2x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Reorder the terms:
8 + 2x + -1x2 = -6 + 6 + -1x + x + x2 + -1x2

Combine like terms: -6 + 6 = 0
8 + 2x + -1x2 = 0 + -1x + x + x2 + -1x2
8 + 2x + -1x2 = -1x + x + x2 + -1x2

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

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

Factor a trinomial.
(4 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {4, -2}