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

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

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

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

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

Multiply 4 * 2
8(2 + x) = (2x + -1)(2x + 1) + -2(x + -1)
(2 * 8 + x * 8) = (2x + -1)(2x + 1) + -2(x + -1)
(16 + 8x) = (2x + -1)(2x + 1) + -2(x + -1)

Reorder the terms:
16 + 8x = (-1 + 2x)(2x + 1) + -2(x + -1)

Reorder the terms:
16 + 8x = (-1 + 2x)(1 + 2x) + -2(x + -1)

Multiply (-1 + 2x) * (1 + 2x)
16 + 8x = (-1(1 + 2x) + 2x * (1 + 2x)) + -2(x + -1)
16 + 8x = ((1 * -1 + 2x * -1) + 2x * (1 + 2x)) + -2(x + -1)
16 + 8x = ((-1 + -2x) + 2x * (1 + 2x)) + -2(x + -1)
16 + 8x = (-1 + -2x + (1 * 2x + 2x * 2x)) + -2(x + -1)
16 + 8x = (-1 + -2x + (2x + 4x2)) + -2(x + -1)

Combine like terms: -2x + 2x = 0
16 + 8x = (-1 + 0 + 4x2) + -2(x + -1)
16 + 8x = (-1 + 4x2) + -2(x + -1)

Reorder the terms:
16 + 8x = -1 + 4x2 + -2(-1 + x)
16 + 8x = -1 + 4x2 + (-1 * -2 + x * -2)
16 + 8x = -1 + 4x2 + (2 + -2x)

Reorder the terms:
16 + 8x = -1 + 2 + -2x + 4x2

Combine like terms: -1 + 2 = 1
16 + 8x = 1 + -2x + 4x2

Solving
16 + 8x = 1 + -2x + 4x2

Solving for variable 'x'.

Reorder the terms:
16 + -1 + 8x + 2x + -4x2 = 1 + -2x + 4x2 + -1 + 2x + -4x2

Combine like terms: 16 + -1 = 15
15 + 8x + 2x + -4x2 = 1 + -2x + 4x2 + -1 + 2x + -4x2

Combine like terms: 8x + 2x = 10x
15 + 10x + -4x2 = 1 + -2x + 4x2 + -1 + 2x + -4x2

Reorder the terms:
15 + 10x + -4x2 = 1 + -1 + -2x + 2x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
15 + 10x + -4x2 = 0 + -2x + 2x + 4x2 + -4x2
15 + 10x + -4x2 = -2x + 2x + 4x2 + -4x2

Combine like terms: -2x + 2x = 0
15 + 10x + -4x2 = 0 + 4x2 + -4x2
15 + 10x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
15 + 10x + -4x2 = 0

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

Divide each side by '-4'.
-3.75 + -2.5x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -2.5x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -2.5x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -2.5x + x2 = 0 + 3.75
-2.5x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-2.5x + x2 = 3.75

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 3.75 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 3.75 + 1.5625

Combine like terms: 3.75 + 1.5625 = 5.3125
1.5625 + -2.5x + x2 = 5.3125

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 5.3125

Calculate the square root of the right side: 2.304886114

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.304886114 and -2.304886114.

Subproblem 1
x + -1.25 = 2.304886114

Simplifying
x + -1.25 = 2.304886114

Reorder the terms:
-1.25 + x = 2.304886114

Solving
-1.25 + x = 2.304886114

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 2.304886114 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 2.304886114 + 1.25
x = 2.304886114 + 1.25

Combine like terms: 2.304886114 + 1.25 = 3.554886114
x = 3.554886114

Simplifying
x = 3.554886114

Subproblem 2
x + -1.25 = -2.304886114

Simplifying
x + -1.25 = -2.304886114

Reorder the terms:
-1.25 + x = -2.304886114

Solving
-1.25 + x = -2.304886114

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -2.304886114 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -2.304886114 + 1.25
x = -2.304886114 + 1.25

Combine like terms: -2.304886114 + 1.25 = -1.054886114
x = -1.054886114

Simplifying
x = -1.054886114

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.554886114, -1.054886114}