(x+3)(x+6)=(2x+2)(x-6)

Solution for (x+3)(x+6)=(2x+2)(x-6) equation:

Simplifying
(x + 3)(x + 6) = (2x + 2)(x + -6)

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

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

Multiply (3 + x) * (6 + x)
(3(6 + x) + x(6 + x)) = (2x + 2)(x + -6)
((6 * 3 + x * 3) + x(6 + x)) = (2x + 2)(x + -6)
((18 + 3x) + x(6 + x)) = (2x + 2)(x + -6)
(18 + 3x + (6 * x + x * x)) = (2x + 2)(x + -6)
(18 + 3x + (6x + x2)) = (2x + 2)(x + -6)

Combine like terms: 3x + 6x = 9x
(18 + 9x + x2) = (2x + 2)(x + -6)

Reorder the terms:
18 + 9x + x2 = (2 + 2x)(x + -6)

Reorder the terms:
18 + 9x + x2 = (2 + 2x)(-6 + x)

Multiply (2 + 2x) * (-6 + x)
18 + 9x + x2 = (2(-6 + x) + 2x * (-6 + x))
18 + 9x + x2 = ((-6 * 2 + x * 2) + 2x * (-6 + x))
18 + 9x + x2 = ((-12 + 2x) + 2x * (-6 + x))
18 + 9x + x2 = (-12 + 2x + (-6 * 2x + x * 2x))
18 + 9x + x2 = (-12 + 2x + (-12x + 2x2))

Combine like terms: 2x + -12x = -10x
18 + 9x + x2 = (-12 + -10x + 2x2)

Solving
18 + 9x + x2 = -12 + -10x + 2x2

Solving for variable 'x'.

Reorder the terms:
18 + 12 + 9x + 10x + x2 + -2x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2

Combine like terms: 18 + 12 = 30
30 + 9x + 10x + x2 + -2x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2

Combine like terms: 9x + 10x = 19x
30 + 19x + x2 + -2x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2

Combine like terms: x2 + -2x2 = -1x2
30 + 19x + -1x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2

Reorder the terms:
30 + 19x + -1x2 = -12 + 12 + -10x + 10x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
30 + 19x + -1x2 = 0 + -10x + 10x + 2x2 + -2x2
30 + 19x + -1x2 = -10x + 10x + 2x2 + -2x2

Combine like terms: -10x + 10x = 0
30 + 19x + -1x2 = 0 + 2x2 + -2x2
30 + 19x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
30 + 19x + -1x2 = 0

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

Divide each side by '-1'.
-30 + -19x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -19x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -19x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -19x + x2 = 0 + 30
-19x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-19x + x2 = 30

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = 30 + 90.25

Reorder the terms:
90.25 + -19x + x2 = 30 + 90.25

Combine like terms: 30 + 90.25 = 120.25
90.25 + -19x + x2 = 120.25

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(x + -9.5) equal to 10.9658561 and -10.9658561.

Subproblem 1
x + -9.5 = 10.9658561

Simplifying
x + -9.5 = 10.9658561

Reorder the terms:
-9.5 + x = 10.9658561

Solving
-9.5 + x = 10.9658561

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = 10.9658561 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 10.9658561 + 9.5
x = 10.9658561 + 9.5

Combine like terms: 10.9658561 + 9.5 = 20.4658561
x = 20.4658561

Simplifying
x = 20.4658561

Subproblem 2
x + -9.5 = -10.9658561

Simplifying
x + -9.5 = -10.9658561

Reorder the terms:
-9.5 + x = -10.9658561

Solving
-9.5 + x = -10.9658561

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = -10.9658561 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -10.9658561 + 9.5
x = -10.9658561 + 9.5

Combine like terms: -10.9658561 + 9.5 = -1.4658561
x = -1.4658561

Simplifying
x = -1.4658561

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.4658561, -1.4658561}