(2x+2)(x+3)-9=(3x-2)(x+2)

Solution for (2x+2)(x+3)-9=(3x-2)(x+2) equation:

Simplifying
(2x + 2)(x + 3) + -9 = (3x + -2)(x + 2)

Reorder the terms:
(2 + 2x)(x + 3) + -9 = (3x + -2)(x + 2)

Reorder the terms:
(2 + 2x)(3 + x) + -9 = (3x + -2)(x + 2)

Multiply (2 + 2x) * (3 + x)
(2(3 + x) + 2x * (3 + x)) + -9 = (3x + -2)(x + 2)
((3 * 2 + x * 2) + 2x * (3 + x)) + -9 = (3x + -2)(x + 2)
((6 + 2x) + 2x * (3 + x)) + -9 = (3x + -2)(x + 2)
(6 + 2x + (3 * 2x + x * 2x)) + -9 = (3x + -2)(x + 2)
(6 + 2x + (6x + 2x2)) + -9 = (3x + -2)(x + 2)

Combine like terms: 2x + 6x = 8x
(6 + 8x + 2x2) + -9 = (3x + -2)(x + 2)

Reorder the terms:
6 + -9 + 8x + 2x2 = (3x + -2)(x + 2)

Combine like terms: 6 + -9 = -3
-3 + 8x + 2x2 = (3x + -2)(x + 2)

Reorder the terms:
-3 + 8x + 2x2 = (-2 + 3x)(x + 2)

Reorder the terms:
-3 + 8x + 2x2 = (-2 + 3x)(2 + x)

Multiply (-2 + 3x) * (2 + x)
-3 + 8x + 2x2 = (-2(2 + x) + 3x * (2 + x))
-3 + 8x + 2x2 = ((2 * -2 + x * -2) + 3x * (2 + x))
-3 + 8x + 2x2 = ((-4 + -2x) + 3x * (2 + x))
-3 + 8x + 2x2 = (-4 + -2x + (2 * 3x + x * 3x))
-3 + 8x + 2x2 = (-4 + -2x + (6x + 3x2))

Combine like terms: -2x + 6x = 4x
-3 + 8x + 2x2 = (-4 + 4x + 3x2)

Solving
-3 + 8x + 2x2 = -4 + 4x + 3x2

Solving for variable 'x'.

Reorder the terms:
-3 + 4 + 8x + -4x + 2x2 + -3x2 = -4 + 4x + 3x2 + 4 + -4x + -3x2

Combine like terms: -3 + 4 = 1
1 + 8x + -4x + 2x2 + -3x2 = -4 + 4x + 3x2 + 4 + -4x + -3x2

Combine like terms: 8x + -4x = 4x
1 + 4x + 2x2 + -3x2 = -4 + 4x + 3x2 + 4 + -4x + -3x2

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

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

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

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

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

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -4x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4x + x2 = 0 + 1

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

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

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1 + 4

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

Combine like terms: 1 + 4 = 5
4 + -4x + x2 = 5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -2) equal to 2.236067978 and -2.236067978.

Subproblem 1
x + -2 = 2.236067978

Simplifying
x + -2 = 2.236067978

Reorder the terms:
-2 + x = 2.236067978

Solving
-2 + x = 2.236067978

Solving for variable 'x'.

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 = 2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.236067978 + 2
x = 2.236067978 + 2

Combine like terms: 2.236067978 + 2 = 4.236067978
x = 4.236067978

Simplifying
x = 4.236067978

Subproblem 2
x + -2 = -2.236067978

Simplifying
x + -2 = -2.236067978

Reorder the terms:
-2 + x = -2.236067978

Solving
-2 + x = -2.236067978

Solving for variable 'x'.

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 = -2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.236067978 + 2
x = -2.236067978 + 2

Combine like terms: -2.236067978 + 2 = -0.236067978
x = -0.236067978

Simplifying
x = -0.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.236067978, -0.236067978}