(2x+3)2=(3x-2)(x+8)+4

Solution for (2x+3)2=(3x-2)(x+8)+4 equation:

Simplifying
(2x + 3) * 2 = (3x + -2)(x + 8) + 4

Reorder the terms:
(3 + 2x) * 2 = (3x + -2)(x + 8) + 4

Reorder the terms for easier multiplication:
2(3 + 2x) = (3x + -2)(x + 8) + 4
(3 * 2 + 2x * 2) = (3x + -2)(x + 8) + 4
(6 + 4x) = (3x + -2)(x + 8) + 4

Reorder the terms:
6 + 4x = (-2 + 3x)(x + 8) + 4

Reorder the terms:
6 + 4x = (-2 + 3x)(8 + x) + 4

Multiply (-2 + 3x) * (8 + x)
6 + 4x = (-2(8 + x) + 3x * (8 + x)) + 4
6 + 4x = ((8 * -2 + x * -2) + 3x * (8 + x)) + 4
6 + 4x = ((-16 + -2x) + 3x * (8 + x)) + 4
6 + 4x = (-16 + -2x + (8 * 3x + x * 3x)) + 4
6 + 4x = (-16 + -2x + (24x + 3x2)) + 4

Combine like terms: -2x + 24x = 22x
6 + 4x = (-16 + 22x + 3x2) + 4

Reorder the terms:
6 + 4x = -16 + 4 + 22x + 3x2

Combine like terms: -16 + 4 = -12
6 + 4x = -12 + 22x + 3x2

Solving
6 + 4x = -12 + 22x + 3x2

Solving for variable 'x'.

Reorder the terms:
6 + 12 + 4x + -22x + -3x2 = -12 + 22x + 3x2 + 12 + -22x + -3x2

Combine like terms: 6 + 12 = 18
18 + 4x + -22x + -3x2 = -12 + 22x + 3x2 + 12 + -22x + -3x2

Combine like terms: 4x + -22x = -18x
18 + -18x + -3x2 = -12 + 22x + 3x2 + 12 + -22x + -3x2

Reorder the terms:
18 + -18x + -3x2 = -12 + 12 + 22x + -22x + 3x2 + -3x2

Combine like terms: -12 + 12 = 0
18 + -18x + -3x2 = 0 + 22x + -22x + 3x2 + -3x2
18 + -18x + -3x2 = 22x + -22x + 3x2 + -3x2

Combine like terms: 22x + -22x = 0
18 + -18x + -3x2 = 0 + 3x2 + -3x2
18 + -18x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
18 + -18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -6x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -6x + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -6x + -1x2 = 0

Solving
6 + -6x + -1x2 = 0

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

Divide each side by '-1'.
-6 + 6x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 6x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 6x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 6x + x2 = 0 + 6
6x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
6x + x2 = 6

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 6 + 9

Reorder the terms:
9 + 6x + x2 = 6 + 9

Combine like terms: 6 + 9 = 15
9 + 6x + x2 = 15

Factor a perfect square on the left side:
(x + 3)(x + 3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + 3) equal to 3.872983346 and -3.872983346.

Subproblem 1
x + 3 = 3.872983346

Simplifying
x + 3 = 3.872983346

Reorder the terms:
3 + x = 3.872983346

Solving
3 + x = 3.872983346

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 3.872983346 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.872983346 + -3
x = 3.872983346 + -3

Combine like terms: 3.872983346 + -3 = 0.872983346
x = 0.872983346

Simplifying
x = 0.872983346

Subproblem 2
x + 3 = -3.872983346

Simplifying
x + 3 = -3.872983346

Reorder the terms:
3 + x = -3.872983346

Solving
3 + x = -3.872983346

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -3.872983346 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.872983346 + -3
x = -3.872983346 + -3

Combine like terms: -3.872983346 + -3 = -6.872983346
x = -6.872983346

Simplifying
x = -6.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.872983346, -6.872983346}
Solution
x = {0.872983346, -6.872983346}