(2x+3)2-(2x-3)(2x+3)=2(3x-5)

Solution for (2x+3)2-(2x-3)(2x+3)=2(3x-5) equation:

Simplifying
(2x + 3) * 2 + -1(2x + -3)(2x + 3) = 2(3x + -5)

Reorder the terms:
(3 + 2x) * 2 + -1(2x + -3)(2x + 3) = 2(3x + -5)

Reorder the terms for easier multiplication:
2(3 + 2x) + -1(2x + -3)(2x + 3) = 2(3x + -5)
(3 * 2 + 2x * 2) + -1(2x + -3)(2x + 3) = 2(3x + -5)
(6 + 4x) + -1(2x + -3)(2x + 3) = 2(3x + -5)

Reorder the terms:
6 + 4x + -1(-3 + 2x)(2x + 3) = 2(3x + -5)

Reorder the terms:
6 + 4x + -1(-3 + 2x)(3 + 2x) = 2(3x + -5)

Multiply (-3 + 2x) * (3 + 2x)
6 + 4x + -1(-3(3 + 2x) + 2x * (3 + 2x)) = 2(3x + -5)
6 + 4x + -1((3 * -3 + 2x * -3) + 2x * (3 + 2x)) = 2(3x + -5)
6 + 4x + -1((-9 + -6x) + 2x * (3 + 2x)) = 2(3x + -5)
6 + 4x + -1(-9 + -6x + (3 * 2x + 2x * 2x)) = 2(3x + -5)
6 + 4x + -1(-9 + -6x + (6x + 4x2)) = 2(3x + -5)

Combine like terms: -6x + 6x = 0
6 + 4x + -1(-9 + 0 + 4x2) = 2(3x + -5)
6 + 4x + -1(-9 + 4x2) = 2(3x + -5)
6 + 4x + (-9 * -1 + 4x2 * -1) = 2(3x + -5)
6 + 4x + (9 + -4x2) = 2(3x + -5)

Reorder the terms:
6 + 9 + 4x + -4x2 = 2(3x + -5)

Combine like terms: 6 + 9 = 15
15 + 4x + -4x2 = 2(3x + -5)

Reorder the terms:
15 + 4x + -4x2 = 2(-5 + 3x)
15 + 4x + -4x2 = (-5 * 2 + 3x * 2)
15 + 4x + -4x2 = (-10 + 6x)

Solving
15 + 4x + -4x2 = -10 + 6x

Solving for variable 'x'.

Reorder the terms:
15 + 10 + 4x + -6x + -4x2 = -10 + 6x + 10 + -6x

Combine like terms: 15 + 10 = 25
25 + 4x + -6x + -4x2 = -10 + 6x + 10 + -6x

Combine like terms: 4x + -6x = -2x
25 + -2x + -4x2 = -10 + 6x + 10 + -6x

Reorder the terms:
25 + -2x + -4x2 = -10 + 10 + 6x + -6x

Combine like terms: -10 + 10 = 0
25 + -2x + -4x2 = 0 + 6x + -6x
25 + -2x + -4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
25 + -2x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-6.25 + 0.5x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 0.5x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 0.5x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 0.5x + x2 = 0 + 6.25
0.5x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
0.5x + x2 = 6.25

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 6.25 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 6.25 + 0.0625

Combine like terms: 6.25 + 0.0625 = 6.3125
0.0625 + 0.5x + x2 = 6.3125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 6.3125

Calculate the square root of the right side: 2.512468905

Break this problem into two subproblems by setting 
(x + 0.25) equal to 2.512468905 and -2.512468905.

Subproblem 1
x + 0.25 = 2.512468905

Simplifying
x + 0.25 = 2.512468905

Reorder the terms:
0.25 + x = 2.512468905

Solving
0.25 + x = 2.512468905

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 2.512468905 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 2.512468905 + -0.25
x = 2.512468905 + -0.25

Combine like terms: 2.512468905 + -0.25 = 2.262468905
x = 2.262468905

Simplifying
x = 2.262468905

Subproblem 2
x + 0.25 = -2.512468905

Simplifying
x + 0.25 = -2.512468905

Reorder the terms:
0.25 + x = -2.512468905

Solving
0.25 + x = -2.512468905

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -2.512468905 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -2.512468905 + -0.25
x = -2.512468905 + -0.25

Combine like terms: -2.512468905 + -0.25 = -2.762468905
x = -2.762468905

Simplifying
x = -2.762468905

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.262468905, -2.762468905}