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

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

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

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

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

Multiply (-5 + 2x) * (5 + 2x)
(-5(5 + 2x) + 2x * (5 + 2x)) + -1(2x + -1) * 2 = x
((5 * -5 + 2x * -5) + 2x * (5 + 2x)) + -1(2x + -1) * 2 = x
((-25 + -10x) + 2x * (5 + 2x)) + -1(2x + -1) * 2 = x
(-25 + -10x + (5 * 2x + 2x * 2x)) + -1(2x + -1) * 2 = x
(-25 + -10x + (10x + 4x2)) + -1(2x + -1) * 2 = x

Combine like terms: -10x + 10x = 0
(-25 + 0 + 4x2) + -1(2x + -1) * 2 = x
(-25 + 4x2) + -1(2x + -1) * 2 = x

Reorder the terms:
-25 + 4x2 + -1(-1 + 2x) * 2 = x

Reorder the terms for easier multiplication:
-25 + 4x2 + -1 * 2(-1 + 2x) = x

Multiply -1 * 2
-25 + 4x2 + -2(-1 + 2x) = x
-25 + 4x2 + (-1 * -2 + 2x * -2) = x
-25 + 4x2 + (2 + -4x) = x

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

Combine like terms: -25 + 2 = -23
-23 + -4x + 4x2 = x

Solving
-23 + -4x + 4x2 = x

Solving for variable 'x'.

Reorder the terms:
-23 + -4x + -1x + 4x2 = x + -1x

Combine like terms: -4x + -1x = -5x
-23 + -5x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
-23 + -5x + 4x2 = 0

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

Divide each side by '4'.
-5.75 + -1.25x + x2 = 0

Move the constant term to the right:

Add '5.75' to each side of the equation.
-5.75 + -1.25x + 5.75 + x2 = 0 + 5.75

Reorder the terms:
-5.75 + 5.75 + -1.25x + x2 = 0 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + -1.25x + x2 = 0 + 5.75
-1.25x + x2 = 0 + 5.75

Combine like terms: 0 + 5.75 = 5.75
-1.25x + x2 = 5.75

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 5.75 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 5.75 + 0.390625

Combine like terms: 5.75 + 0.390625 = 6.140625
0.390625 + -1.25x + x2 = 6.140625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 6.140625

Calculate the square root of the right side: 2.47802845

Break this problem into two subproblems by setting 
(x + -0.625) equal to 2.47802845 and -2.47802845.

Subproblem 1
x + -0.625 = 2.47802845

Simplifying
x + -0.625 = 2.47802845

Reorder the terms:
-0.625 + x = 2.47802845

Solving
-0.625 + x = 2.47802845

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 2.47802845 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 2.47802845 + 0.625
x = 2.47802845 + 0.625

Combine like terms: 2.47802845 + 0.625 = 3.10302845
x = 3.10302845

Simplifying
x = 3.10302845

Subproblem 2
x + -0.625 = -2.47802845

Simplifying
x + -0.625 = -2.47802845

Reorder the terms:
-0.625 + x = -2.47802845

Solving
-0.625 + x = -2.47802845

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -2.47802845 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -2.47802845 + 0.625
x = -2.47802845 + 0.625

Combine like terms: -2.47802845 + 0.625 = -1.85302845
x = -1.85302845

Simplifying
x = -1.85302845

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.10302845, -1.85302845}