(20)(36)=(2x-6)(x+8)

Solution for (20)(36)=(2x-6)(x+8) equation:

Simplifying
(20)(36) = (2x + -6)(x + 8)

Multiply 20 * 36
720 = (2x + -6)(x + 8)

Reorder the terms:
720 = (-6 + 2x)(x + 8)

Reorder the terms:
720 = (-6 + 2x)(8 + x)

Multiply (-6 + 2x) * (8 + x)
720 = (-6(8 + x) + 2x * (8 + x))
720 = ((8 * -6 + x * -6) + 2x * (8 + x))
720 = ((-48 + -6x) + 2x * (8 + x))
720 = (-48 + -6x + (8 * 2x + x * 2x))
720 = (-48 + -6x + (16x + 2x2))

Combine like terms: -6x + 16x = 10x
720 = (-48 + 10x + 2x2)

Solving
720 = -48 + 10x + 2x2

Solving for variable 'x'.

Combine like terms: 720 + 48 = 768
768 + -10x + -2x2 = -48 + 10x + 2x2 + 48 + -10x + -2x2

Reorder the terms:
768 + -10x + -2x2 = -48 + 48 + 10x + -10x + 2x2 + -2x2

Combine like terms: -48 + 48 = 0
768 + -10x + -2x2 = 0 + 10x + -10x + 2x2 + -2x2
768 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
768 + -10x + -2x2 = 0 + 2x2 + -2x2
768 + -10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
768 + -10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(384 + -5x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(384 + -5x + -1x2)' equal to zero and attempt to solve:

Simplifying
384 + -5x + -1x2 = 0

Solving
384 + -5x + -1x2 = 0

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

Divide each side by '-1'.
-384 + 5x + x2 = 0

Move the constant term to the right:

Add '384' to each side of the equation.
-384 + 5x + 384 + x2 = 0 + 384

Reorder the terms:
-384 + 384 + 5x + x2 = 0 + 384

Combine like terms: -384 + 384 = 0
0 + 5x + x2 = 0 + 384
5x + x2 = 0 + 384

Combine like terms: 0 + 384 = 384
5x + x2 = 384

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 384 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 384 + 6.25

Combine like terms: 384 + 6.25 = 390.25
6.25 + 5x + x2 = 390.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 390.25

Calculate the square root of the right side: 19.754746265

Break this problem into two subproblems by setting 
(x + 2.5) equal to 19.754746265 and -19.754746265.

Subproblem 1
x + 2.5 = 19.754746265

Simplifying
x + 2.5 = 19.754746265

Reorder the terms:
2.5 + x = 19.754746265

Solving
2.5 + x = 19.754746265

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 19.754746265 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 19.754746265 + -2.5
x = 19.754746265 + -2.5

Combine like terms: 19.754746265 + -2.5 = 17.254746265
x = 17.254746265

Simplifying
x = 17.254746265

Subproblem 2
x + 2.5 = -19.754746265

Simplifying
x + 2.5 = -19.754746265

Reorder the terms:
2.5 + x = -19.754746265

Solving
2.5 + x = -19.754746265

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -19.754746265 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -19.754746265 + -2.5
x = -19.754746265 + -2.5

Combine like terms: -19.754746265 + -2.5 = -22.254746265
x = -22.254746265

Simplifying
x = -22.254746265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.254746265, -22.254746265}
Solution
x = {17.254746265, -22.254746265}