(5x+20)(x+40)=180

Solution for (5x+20)(x+40)=180 equation:

Simplifying
(5x + 20)(x + 40) = 180

Reorder the terms:
(20 + 5x)(x + 40) = 180

Reorder the terms:
(20 + 5x)(40 + x) = 180

Multiply (20 + 5x) * (40 + x)
(20(40 + x) + 5x * (40 + x)) = 180
((40 * 20 + x * 20) + 5x * (40 + x)) = 180
((800 + 20x) + 5x * (40 + x)) = 180
(800 + 20x + (40 * 5x + x * 5x)) = 180
(800 + 20x + (200x + 5x2)) = 180

Combine like terms: 20x + 200x = 220x
(800 + 220x + 5x2) = 180

Solving
800 + 220x + 5x2 = 180

Solving for variable 'x'.

Reorder the terms:
800 + -180 + 220x + 5x2 = 180 + -180

Combine like terms: 800 + -180 = 620
620 + 220x + 5x2 = 180 + -180

Combine like terms: 180 + -180 = 0
620 + 220x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(124 + 44x + x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(124 + 44x + x2)' equal to zero and attempt to solve:

Simplifying
124 + 44x + x2 = 0

Solving
124 + 44x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-124' to each side of the equation.
124 + 44x + -124 + x2 = 0 + -124

Reorder the terms:
124 + -124 + 44x + x2 = 0 + -124

Combine like terms: 124 + -124 = 0
0 + 44x + x2 = 0 + -124
44x + x2 = 0 + -124

Combine like terms: 0 + -124 = -124
44x + x2 = -124

The x term is 44x.  Take half its coefficient (22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
44x + 484 + x2 = -124 + 484

Reorder the terms:
484 + 44x + x2 = -124 + 484

Combine like terms: -124 + 484 = 360
484 + 44x + x2 = 360

Factor a perfect square on the left side:
(x + 22)(x + 22) = 360

Calculate the square root of the right side: 18.973665961

Break this problem into two subproblems by setting 
(x + 22) equal to 18.973665961 and -18.973665961.

Subproblem 1
x + 22 = 18.973665961

Simplifying
x + 22 = 18.973665961

Reorder the terms:
22 + x = 18.973665961

Solving
22 + x = 18.973665961

Solving for variable 'x'.

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

Add '-22' to each side of the equation.
22 + -22 + x = 18.973665961 + -22

Combine like terms: 22 + -22 = 0
0 + x = 18.973665961 + -22
x = 18.973665961 + -22

Combine like terms: 18.973665961 + -22 = -3.026334039
x = -3.026334039

Simplifying
x = -3.026334039

Subproblem 2
x + 22 = -18.973665961

Simplifying
x + 22 = -18.973665961

Reorder the terms:
22 + x = -18.973665961

Solving
22 + x = -18.973665961

Solving for variable 'x'.

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

Add '-22' to each side of the equation.
22 + -22 + x = -18.973665961 + -22

Combine like terms: 22 + -22 = 0
0 + x = -18.973665961 + -22
x = -18.973665961 + -22

Combine like terms: -18.973665961 + -22 = -40.973665961
x = -40.973665961

Simplifying
x = -40.973665961

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.026334039, -40.973665961}
Solution
x = {-3.026334039, -40.973665961}