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

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

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

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

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

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

Combine like terms: 6x + 2x = 8x
(12 + 8x + x2) = (2x + 1)(x + -2)

Reorder the terms:
12 + 8x + x2 = (1 + 2x)(x + -2)

Reorder the terms:
12 + 8x + x2 = (1 + 2x)(-2 + x)

Multiply (1 + 2x) * (-2 + x)
12 + 8x + x2 = (1(-2 + x) + 2x * (-2 + x))
12 + 8x + x2 = ((-2 * 1 + x * 1) + 2x * (-2 + x))
12 + 8x + x2 = ((-2 + 1x) + 2x * (-2 + x))
12 + 8x + x2 = (-2 + 1x + (-2 * 2x + x * 2x))
12 + 8x + x2 = (-2 + 1x + (-4x + 2x2))

Combine like terms: 1x + -4x = -3x
12 + 8x + x2 = (-2 + -3x + 2x2)

Solving
12 + 8x + x2 = -2 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
12 + 2 + 8x + 3x + x2 + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2

Combine like terms: 12 + 2 = 14
14 + 8x + 3x + x2 + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2

Combine like terms: 8x + 3x = 11x
14 + 11x + x2 + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2

Combine like terms: x2 + -2x2 = -1x2
14 + 11x + -1x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2

Reorder the terms:
14 + 11x + -1x2 = -2 + 2 + -3x + 3x + 2x2 + -2x2

Combine like terms: -2 + 2 = 0
14 + 11x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2
14 + 11x + -1x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
14 + 11x + -1x2 = 0 + 2x2 + -2x2
14 + 11x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
14 + 11x + -1x2 = 0

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

Divide each side by '-1'.
-14 + -11x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -11x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -11x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -11x + x2 = 0 + 14
-11x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-11x + x2 = 14

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 = 14 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 14 + 30.25

Combine like terms: 14 + 30.25 = 44.25
30.25 + -11x + x2 = 44.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(x + -5.5) equal to 6.652067348 and -6.652067348.

Subproblem 1
x + -5.5 = 6.652067348

Simplifying
x + -5.5 = 6.652067348

Reorder the terms:
-5.5 + x = 6.652067348

Solving
-5.5 + x = 6.652067348

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 = 6.652067348 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 6.652067348 + 5.5
x = 6.652067348 + 5.5

Combine like terms: 6.652067348 + 5.5 = 12.152067348
x = 12.152067348

Simplifying
x = 12.152067348

Subproblem 2
x + -5.5 = -6.652067348

Simplifying
x + -5.5 = -6.652067348

Reorder the terms:
-5.5 + x = -6.652067348

Solving
-5.5 + x = -6.652067348

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 = -6.652067348 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -6.652067348 + 5.5
x = -6.652067348 + 5.5

Combine like terms: -6.652067348 + 5.5 = -1.152067348
x = -1.152067348

Simplifying
x = -1.152067348

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.152067348, -1.152067348}