(x-6)(2x+6)=(x-9)(x-4)

Solution for (x-6)(2x+6)=(x-9)(x-4) equation:

Simplifying
(x + -6)(2x + 6) = (x + -9)(x + -4)

Reorder the terms:
(-6 + x)(2x + 6) = (x + -9)(x + -4)

Reorder the terms:
(-6 + x)(6 + 2x) = (x + -9)(x + -4)

Multiply (-6 + x) * (6 + 2x)
(-6(6 + 2x) + x(6 + 2x)) = (x + -9)(x + -4)
((6 * -6 + 2x * -6) + x(6 + 2x)) = (x + -9)(x + -4)
((-36 + -12x) + x(6 + 2x)) = (x + -9)(x + -4)
(-36 + -12x + (6 * x + 2x * x)) = (x + -9)(x + -4)
(-36 + -12x + (6x + 2x2)) = (x + -9)(x + -4)

Combine like terms: -12x + 6x = -6x
(-36 + -6x + 2x2) = (x + -9)(x + -4)

Reorder the terms:
-36 + -6x + 2x2 = (-9 + x)(x + -4)

Reorder the terms:
-36 + -6x + 2x2 = (-9 + x)(-4 + x)

Multiply (-9 + x) * (-4 + x)
-36 + -6x + 2x2 = (-9(-4 + x) + x(-4 + x))
-36 + -6x + 2x2 = ((-4 * -9 + x * -9) + x(-4 + x))
-36 + -6x + 2x2 = ((36 + -9x) + x(-4 + x))
-36 + -6x + 2x2 = (36 + -9x + (-4 * x + x * x))
-36 + -6x + 2x2 = (36 + -9x + (-4x + x2))

Combine like terms: -9x + -4x = -13x
-36 + -6x + 2x2 = (36 + -13x + x2)

Solving
-36 + -6x + 2x2 = 36 + -13x + x2

Solving for variable 'x'.

Reorder the terms:
-36 + -36 + -6x + 13x + 2x2 + -1x2 = 36 + -13x + x2 + -36 + 13x + -1x2

Combine like terms: -36 + -36 = -72
-72 + -6x + 13x + 2x2 + -1x2 = 36 + -13x + x2 + -36 + 13x + -1x2

Combine like terms: -6x + 13x = 7x
-72 + 7x + 2x2 + -1x2 = 36 + -13x + x2 + -36 + 13x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-72 + 7x + 1x2 = 36 + -13x + x2 + -36 + 13x + -1x2

Reorder the terms:
-72 + 7x + 1x2 = 36 + -36 + -13x + 13x + x2 + -1x2

Combine like terms: 36 + -36 = 0
-72 + 7x + 1x2 = 0 + -13x + 13x + x2 + -1x2
-72 + 7x + 1x2 = -13x + 13x + x2 + -1x2

Combine like terms: -13x + 13x = 0
-72 + 7x + 1x2 = 0 + x2 + -1x2
-72 + 7x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-72 + 7x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 7x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + 7x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 7x + x2 = 0 + 72
7x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
7x + x2 = 72

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 72 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 72 + 12.25

Combine like terms: 72 + 12.25 = 84.25
12.25 + 7x + x2 = 84.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 84.25

Calculate the square root of the right side: 9.178779875

Break this problem into two subproblems by setting 
(x + 3.5) equal to 9.178779875 and -9.178779875.

Subproblem 1
x + 3.5 = 9.178779875

Simplifying
x + 3.5 = 9.178779875

Reorder the terms:
3.5 + x = 9.178779875

Solving
3.5 + x = 9.178779875

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 9.178779875 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 9.178779875 + -3.5
x = 9.178779875 + -3.5

Combine like terms: 9.178779875 + -3.5 = 5.678779875
x = 5.678779875

Simplifying
x = 5.678779875

Subproblem 2
x + 3.5 = -9.178779875

Simplifying
x + 3.5 = -9.178779875

Reorder the terms:
3.5 + x = -9.178779875

Solving
3.5 + x = -9.178779875

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -9.178779875 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -9.178779875 + -3.5
x = -9.178779875 + -3.5

Combine like terms: -9.178779875 + -3.5 = -12.678779875
x = -12.678779875

Simplifying
x = -12.678779875

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.678779875, -12.678779875}