(2x+1)(2x+3)=13(2x+5)+26

Solution for (2x+1)(2x+3)=13(2x+5)+26 equation:

Simplifying
(2x + 1)(2x + 3) = 13(2x + 5) + 26

Reorder the terms:
(1 + 2x)(2x + 3) = 13(2x + 5) + 26

Reorder the terms:
(1 + 2x)(3 + 2x) = 13(2x + 5) + 26

Multiply (1 + 2x) * (3 + 2x)
(1(3 + 2x) + 2x * (3 + 2x)) = 13(2x + 5) + 26
((3 * 1 + 2x * 1) + 2x * (3 + 2x)) = 13(2x + 5) + 26
((3 + 2x) + 2x * (3 + 2x)) = 13(2x + 5) + 26
(3 + 2x + (3 * 2x + 2x * 2x)) = 13(2x + 5) + 26
(3 + 2x + (6x + 4x2)) = 13(2x + 5) + 26

Combine like terms: 2x + 6x = 8x
(3 + 8x + 4x2) = 13(2x + 5) + 26

Reorder the terms:
3 + 8x + 4x2 = 13(5 + 2x) + 26
3 + 8x + 4x2 = (5 * 13 + 2x * 13) + 26
3 + 8x + 4x2 = (65 + 26x) + 26

Reorder the terms:
3 + 8x + 4x2 = 65 + 26 + 26x

Combine like terms: 65 + 26 = 91
3 + 8x + 4x2 = 91 + 26x

Solving
3 + 8x + 4x2 = 91 + 26x

Solving for variable 'x'.

Reorder the terms:
3 + -91 + 8x + -26x + 4x2 = 91 + 26x + -91 + -26x

Combine like terms: 3 + -91 = -88
-88 + 8x + -26x + 4x2 = 91 + 26x + -91 + -26x

Combine like terms: 8x + -26x = -18x
-88 + -18x + 4x2 = 91 + 26x + -91 + -26x

Reorder the terms:
-88 + -18x + 4x2 = 91 + -91 + 26x + -26x

Combine like terms: 91 + -91 = 0
-88 + -18x + 4x2 = 0 + 26x + -26x
-88 + -18x + 4x2 = 26x + -26x

Combine like terms: 26x + -26x = 0
-88 + -18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-44 + -9x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-44 + -9x + 2x2)' equal to zero and attempt to solve:

Simplifying
-44 + -9x + 2x2 = 0

Solving
-44 + -9x + 2x2 = 0

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

Divide each side by '2'.
-22 + -4.5x + x2 = 0

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -4.5x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + -4.5x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -4.5x + x2 = 0 + 22
-4.5x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
-4.5x + x2 = 22

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 22 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 22 + 5.0625

Combine like terms: 22 + 5.0625 = 27.0625
5.0625 + -4.5x + x2 = 27.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 27.0625

Calculate the square root of the right side: 5.202163012

Break this problem into two subproblems by setting 
(x + -2.25) equal to 5.202163012 and -5.202163012.

Subproblem 1
x + -2.25 = 5.202163012

Simplifying
x + -2.25 = 5.202163012

Reorder the terms:
-2.25 + x = 5.202163012

Solving
-2.25 + x = 5.202163012

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 5.202163012 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 5.202163012 + 2.25
x = 5.202163012 + 2.25

Combine like terms: 5.202163012 + 2.25 = 7.452163012
x = 7.452163012

Simplifying
x = 7.452163012

Subproblem 2
x + -2.25 = -5.202163012

Simplifying
x + -2.25 = -5.202163012

Reorder the terms:
-2.25 + x = -5.202163012

Solving
-2.25 + x = -5.202163012

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -5.202163012 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -5.202163012 + 2.25
x = -5.202163012 + 2.25

Combine like terms: -5.202163012 + 2.25 = -2.952163012
x = -2.952163012

Simplifying
x = -2.952163012

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.452163012, -2.952163012}
Solution
x = {7.452163012, -2.952163012}