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

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

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

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

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

Combine like terms: 2x + 6x = 8x
9 + 8x = (4x + -3)(x + 2)

Reorder the terms:
9 + 8x = (-3 + 4x)(x + 2)

Reorder the terms:
9 + 8x = (-3 + 4x)(2 + x)

Multiply (-3 + 4x) * (2 + x)
9 + 8x = (-3(2 + x) + 4x * (2 + x))
9 + 8x = ((2 * -3 + x * -3) + 4x * (2 + x))
9 + 8x = ((-6 + -3x) + 4x * (2 + x))
9 + 8x = (-6 + -3x + (2 * 4x + x * 4x))
9 + 8x = (-6 + -3x + (8x + 4x2))

Combine like terms: -3x + 8x = 5x
9 + 8x = (-6 + 5x + 4x2)

Solving
9 + 8x = -6 + 5x + 4x2

Solving for variable 'x'.

Reorder the terms:
9 + 6 + 8x + -5x + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2

Combine like terms: 9 + 6 = 15
15 + 8x + -5x + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2

Combine like terms: 8x + -5x = 3x
15 + 3x + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2

Reorder the terms:
15 + 3x + -4x2 = -6 + 6 + 5x + -5x + 4x2 + -4x2

Combine like terms: -6 + 6 = 0
15 + 3x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2
15 + 3x + -4x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
15 + 3x + -4x2 = 0 + 4x2 + -4x2
15 + 3x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
15 + 3x + -4x2 = 0

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

Divide each side by '-4'.
-3.75 + -0.75x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -0.75x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -0.75x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -0.75x + x2 = 0 + 3.75
-0.75x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-0.75x + x2 = 3.75

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 3.75 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 3.75 + 0.140625

Combine like terms: 3.75 + 0.140625 = 3.890625
0.140625 + -0.75x + x2 = 3.890625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 3.890625

Calculate the square root of the right side: 1.97246673

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.97246673 and -1.97246673.

Subproblem 1
x + -0.375 = 1.97246673

Simplifying
x + -0.375 = 1.97246673

Reorder the terms:
-0.375 + x = 1.97246673

Solving
-0.375 + x = 1.97246673

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 1.97246673 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.97246673 + 0.375
x = 1.97246673 + 0.375

Combine like terms: 1.97246673 + 0.375 = 2.34746673
x = 2.34746673

Simplifying
x = 2.34746673

Subproblem 2
x + -0.375 = -1.97246673

Simplifying
x + -0.375 = -1.97246673

Reorder the terms:
-0.375 + x = -1.97246673

Solving
-0.375 + x = -1.97246673

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -1.97246673 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.97246673 + 0.375
x = -1.97246673 + 0.375

Combine like terms: -1.97246673 + 0.375 = -1.59746673
x = -1.59746673

Simplifying
x = -1.59746673

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.34746673, -1.59746673}