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

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

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

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

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

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

Combine like terms: -2x + 2x = 0
(-1 + 0 + 4x2) + -1(4x + 5) * 2 = -4x + -2
(-1 + 4x2) + -1(4x + 5) * 2 = -4x + -2

Reorder the terms:
-1 + 4x2 + -1(5 + 4x) * 2 = -4x + -2

Reorder the terms for easier multiplication:
-1 + 4x2 + -1 * 2(5 + 4x) = -4x + -2

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

Reorder the terms:
-1 + -10 + -8x + 4x2 = -4x + -2

Combine like terms: -1 + -10 = -11
-11 + -8x + 4x2 = -4x + -2

Reorder the terms:
-11 + -8x + 4x2 = -2 + -4x

Solving
-11 + -8x + 4x2 = -2 + -4x

Solving for variable 'x'.

Reorder the terms:
-11 + 2 + -8x + 4x + 4x2 = -2 + -4x + 2 + 4x

Combine like terms: -11 + 2 = -9
-9 + -8x + 4x + 4x2 = -2 + -4x + 2 + 4x

Combine like terms: -8x + 4x = -4x
-9 + -4x + 4x2 = -2 + -4x + 2 + 4x

Reorder the terms:
-9 + -4x + 4x2 = -2 + 2 + -4x + 4x

Combine like terms: -2 + 2 = 0
-9 + -4x + 4x2 = 0 + -4x + 4x
-9 + -4x + 4x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-9 + -4x + 4x2 = 0

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

Divide each side by '4'.
-2.25 + -1x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -1x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -1x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -1x + x2 = 0 + 2.25
-1x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-1x + x2 = 2.25

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 2.25 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 2.25 + 0.25

Combine like terms: 2.25 + 0.25 = 2.5
0.25 + -1x + x2 = 2.5

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.58113883 and -1.58113883.

Subproblem 1
x + -0.5 = 1.58113883

Simplifying
x + -0.5 = 1.58113883

Reorder the terms:
-0.5 + x = 1.58113883

Solving
-0.5 + x = 1.58113883

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 1.58113883 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.58113883 + 0.5
x = 1.58113883 + 0.5

Combine like terms: 1.58113883 + 0.5 = 2.08113883
x = 2.08113883

Simplifying
x = 2.08113883

Subproblem 2
x + -0.5 = -1.58113883

Simplifying
x + -0.5 = -1.58113883

Reorder the terms:
-0.5 + x = -1.58113883

Solving
-0.5 + x = -1.58113883

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -1.58113883 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.58113883 + 0.5
x = -1.58113883 + 0.5

Combine like terms: -1.58113883 + 0.5 = -1.08113883
x = -1.08113883

Simplifying
x = -1.08113883

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.08113883, -1.08113883}