(2x+5)(2x-4)=(2x+1)2

Solution for (2x+5)(2x-4)=(2x+1)2 equation:

Simplifying
(2x + 5)(2x + -4) = (2x + 1) * 2

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

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

Multiply (5 + 2x) * (-4 + 2x)
(5(-4 + 2x) + 2x * (-4 + 2x)) = (2x + 1) * 2
((-4 * 5 + 2x * 5) + 2x * (-4 + 2x)) = (2x + 1) * 2
((-20 + 10x) + 2x * (-4 + 2x)) = (2x + 1) * 2
(-20 + 10x + (-4 * 2x + 2x * 2x)) = (2x + 1) * 2
(-20 + 10x + (-8x + 4x2)) = (2x + 1) * 2

Combine like terms: 10x + -8x = 2x
(-20 + 2x + 4x2) = (2x + 1) * 2

Reorder the terms:
-20 + 2x + 4x2 = (1 + 2x) * 2

Reorder the terms for easier multiplication:
-20 + 2x + 4x2 = 2(1 + 2x)
-20 + 2x + 4x2 = (1 * 2 + 2x * 2)
-20 + 2x + 4x2 = (2 + 4x)

Solving
-20 + 2x + 4x2 = 2 + 4x

Solving for variable 'x'.

Reorder the terms:
-20 + -2 + 2x + -4x + 4x2 = 2 + 4x + -2 + -4x

Combine like terms: -20 + -2 = -22
-22 + 2x + -4x + 4x2 = 2 + 4x + -2 + -4x

Combine like terms: 2x + -4x = -2x
-22 + -2x + 4x2 = 2 + 4x + -2 + -4x

Reorder the terms:
-22 + -2x + 4x2 = 2 + -2 + 4x + -4x

Combine like terms: 2 + -2 = 0
-22 + -2x + 4x2 = 0 + 4x + -4x
-22 + -2x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-22 + -2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + -1x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying
-11 + -1x + 2x2 = 0

Solving
-11 + -1x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -0.5x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -0.5x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -0.5x + x2 = 0 + 5.5
-0.5x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-0.5x + x2 = 5.5

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 = 5.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 5.5 + 0.0625

Combine like terms: 5.5 + 0.0625 = 5.5625
0.0625 + -0.5x + x2 = 5.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.358495283 and -2.358495283.

Subproblem 1
x + -0.25 = 2.358495283

Simplifying
x + -0.25 = 2.358495283

Reorder the terms:
-0.25 + x = 2.358495283

Solving
-0.25 + x = 2.358495283

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 = 2.358495283 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 2.358495283 + 0.25
x = 2.358495283 + 0.25

Combine like terms: 2.358495283 + 0.25 = 2.608495283
x = 2.608495283

Simplifying
x = 2.608495283

Subproblem 2
x + -0.25 = -2.358495283

Simplifying
x + -0.25 = -2.358495283

Reorder the terms:
-0.25 + x = -2.358495283

Solving
-0.25 + x = -2.358495283

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 = -2.358495283 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -2.358495283 + 0.25
x = -2.358495283 + 0.25

Combine like terms: -2.358495283 + 0.25 = -2.108495283
x = -2.108495283

Simplifying
x = -2.108495283

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.608495283, -2.108495283}
Solution
x = {2.608495283, -2.108495283}