(6x+20)(4x+20)=180

Solution for (6x+20)(4x+20)=180 equation:

Simplifying
(6x + 20)(4x + 20) = 180

Reorder the terms:
(20 + 6x)(4x + 20) = 180

Reorder the terms:
(20 + 6x)(20 + 4x) = 180

Multiply (20 + 6x) * (20 + 4x)
(20(20 + 4x) + 6x * (20 + 4x)) = 180
((20 * 20 + 4x * 20) + 6x * (20 + 4x)) = 180
((400 + 80x) + 6x * (20 + 4x)) = 180
(400 + 80x + (20 * 6x + 4x * 6x)) = 180
(400 + 80x + (120x + 24x2)) = 180

Combine like terms: 80x + 120x = 200x
(400 + 200x + 24x2) = 180

Solving
400 + 200x + 24x2 = 180

Solving for variable 'x'.

Reorder the terms:
400 + -180 + 200x + 24x2 = 180 + -180

Combine like terms: 400 + -180 = 220
220 + 200x + 24x2 = 180 + -180

Combine like terms: 180 + -180 = 0
220 + 200x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(55 + 50x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(55 + 50x + 6x2)' equal to zero and attempt to solve:

Simplifying
55 + 50x + 6x2 = 0

Solving
55 + 50x + 6x2 = 0

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

Divide each side by '6'.
9.166666667 + 8.333333333x + x2 = 0

Move the constant term to the right:

Add '-9.166666667' to each side of the equation.
9.166666667 + 8.333333333x + -9.166666667 + x2 = 0 + -9.166666667

Reorder the terms:
9.166666667 + -9.166666667 + 8.333333333x + x2 = 0 + -9.166666667

Combine like terms: 9.166666667 + -9.166666667 = 0.000000000
0.000000000 + 8.333333333x + x2 = 0 + -9.166666667
8.333333333x + x2 = 0 + -9.166666667

Combine like terms: 0 + -9.166666667 = -9.166666667
8.333333333x + x2 = -9.166666667

The x term is 8.333333333x.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333x + 17.36111111 + x2 = -9.166666667 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333x + x2 = -9.166666667 + 17.36111111

Combine like terms: -9.166666667 + 17.36111111 = 8.194444443
17.36111111 + 8.333333333x + x2 = 8.194444443

Factor a perfect square on the left side:
(x + 4.166666667)(x + 4.166666667) = 8.194444443

Calculate the square root of the right side: 2.862594006

Break this problem into two subproblems by setting 
(x + 4.166666667) equal to 2.862594006 and -2.862594006.

Subproblem 1
x + 4.166666667 = 2.862594006

Simplifying
x + 4.166666667 = 2.862594006

Reorder the terms:
4.166666667 + x = 2.862594006

Solving
4.166666667 + x = 2.862594006

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = 2.862594006 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = 2.862594006 + -4.166666667
x = 2.862594006 + -4.166666667

Combine like terms: 2.862594006 + -4.166666667 = -1.304072661
x = -1.304072661

Simplifying
x = -1.304072661

Subproblem 2
x + 4.166666667 = -2.862594006

Simplifying
x + 4.166666667 = -2.862594006

Reorder the terms:
4.166666667 + x = -2.862594006

Solving
4.166666667 + x = -2.862594006

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = -2.862594006 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = -2.862594006 + -4.166666667
x = -2.862594006 + -4.166666667

Combine like terms: -2.862594006 + -4.166666667 = -7.029260673
x = -7.029260673

Simplifying
x = -7.029260673

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.304072661, -7.029260673}
Solution
x = {-1.304072661, -7.029260673}