(x+2)(x-2)=(2x+1)(x-6)

Solution for (x+2)(x-2)=(2x+1)(x-6) equation:

Simplifying
(x + 2)(x + -2) = (2x + 1)(x + -6)

Reorder the terms:
(2 + x)(x + -2) = (2x + 1)(x + -6)

Reorder the terms:
(2 + x)(-2 + x) = (2x + 1)(x + -6)

Multiply (2 + x) * (-2 + x)
(2(-2 + x) + x(-2 + x)) = (2x + 1)(x + -6)
((-2 * 2 + x * 2) + x(-2 + x)) = (2x + 1)(x + -6)
((-4 + 2x) + x(-2 + x)) = (2x + 1)(x + -6)
(-4 + 2x + (-2 * x + x * x)) = (2x + 1)(x + -6)
(-4 + 2x + (-2x + x2)) = (2x + 1)(x + -6)

Combine like terms: 2x + -2x = 0
(-4 + 0 + x2) = (2x + 1)(x + -6)
(-4 + x2) = (2x + 1)(x + -6)

Reorder the terms:
-4 + x2 = (1 + 2x)(x + -6)

Reorder the terms:
-4 + x2 = (1 + 2x)(-6 + x)

Multiply (1 + 2x) * (-6 + x)
-4 + x2 = (1(-6 + x) + 2x * (-6 + x))
-4 + x2 = ((-6 * 1 + x * 1) + 2x * (-6 + x))
-4 + x2 = ((-6 + 1x) + 2x * (-6 + x))
-4 + x2 = (-6 + 1x + (-6 * 2x + x * 2x))
-4 + x2 = (-6 + 1x + (-12x + 2x2))

Combine like terms: 1x + -12x = -11x
-4 + x2 = (-6 + -11x + 2x2)

Solving
-4 + x2 = -6 + -11x + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + 6 + 11x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2

Combine like terms: -4 + 6 = 2
2 + 11x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2

Combine like terms: x2 + -2x2 = -1x2
2 + 11x + -1x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2

Reorder the terms:
2 + 11x + -1x2 = -6 + 6 + -11x + 11x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
2 + 11x + -1x2 = 0 + -11x + 11x + 2x2 + -2x2
2 + 11x + -1x2 = -11x + 11x + 2x2 + -2x2

Combine like terms: -11x + 11x = 0
2 + 11x + -1x2 = 0 + 2x2 + -2x2
2 + 11x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
2 + 11x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -11x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -11x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -11x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -11x + x2 = 0 + 2
-11x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-11x + x2 = 2

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 2 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 2 + 30.25

Combine like terms: 2 + 30.25 = 32.25
30.25 + -11x + x2 = 32.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
x + -5.5 = 5.678908346

Simplifying
x + -5.5 = 5.678908346

Reorder the terms:
-5.5 + x = 5.678908346

Solving
-5.5 + x = 5.678908346

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 5.678908346 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 5.678908346 + 5.5
x = 5.678908346 + 5.5

Combine like terms: 5.678908346 + 5.5 = 11.178908346
x = 11.178908346

Simplifying
x = 11.178908346

Subproblem 2
x + -5.5 = -5.678908346

Simplifying
x + -5.5 = -5.678908346

Reorder the terms:
-5.5 + x = -5.678908346

Solving
-5.5 + x = -5.678908346

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -5.678908346 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -5.678908346 + 5.5
x = -5.678908346 + 5.5

Combine like terms: -5.678908346 + 5.5 = -0.178908346
x = -0.178908346

Simplifying
x = -0.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.178908346, -0.178908346}