(2x+24)(4x+36)=180

Solution for (2x+24)(4x+36)=180 equation:

Simplifying
(2x + 24)(4x + 36) = 180

Reorder the terms:
(24 + 2x)(4x + 36) = 180

Reorder the terms:
(24 + 2x)(36 + 4x) = 180

Multiply (24 + 2x) * (36 + 4x)
(24(36 + 4x) + 2x * (36 + 4x)) = 180
((36 * 24 + 4x * 24) + 2x * (36 + 4x)) = 180
((864 + 96x) + 2x * (36 + 4x)) = 180
(864 + 96x + (36 * 2x + 4x * 2x)) = 180
(864 + 96x + (72x + 8x2)) = 180

Combine like terms: 96x + 72x = 168x
(864 + 168x + 8x2) = 180

Solving
864 + 168x + 8x2 = 180

Solving for variable 'x'.

Reorder the terms:
864 + -180 + 168x + 8x2 = 180 + -180

Combine like terms: 864 + -180 = 684
684 + 168x + 8x2 = 180 + -180

Combine like terms: 180 + -180 = 0
684 + 168x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(171 + 42x + 2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(171 + 42x + 2x2)' equal to zero and attempt to solve:

Simplifying
171 + 42x + 2x2 = 0

Solving
171 + 42x + 2x2 = 0

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

Divide each side by '2'.
85.5 + 21x + x2 = 0

Move the constant term to the right:

Add '-85.5' to each side of the equation.
85.5 + 21x + -85.5 + x2 = 0 + -85.5

Reorder the terms:
85.5 + -85.5 + 21x + x2 = 0 + -85.5

Combine like terms: 85.5 + -85.5 = 0.0
0.0 + 21x + x2 = 0 + -85.5
21x + x2 = 0 + -85.5

Combine like terms: 0 + -85.5 = -85.5
21x + x2 = -85.5

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = -85.5 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -85.5 + 110.25

Combine like terms: -85.5 + 110.25 = 24.75
110.25 + 21x + x2 = 24.75

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 24.75

Calculate the square root of the right side: 4.974937186

Break this problem into two subproblems by setting 
(x + 10.5) equal to 4.974937186 and -4.974937186.

Subproblem 1
x + 10.5 = 4.974937186

Simplifying
x + 10.5 = 4.974937186

Reorder the terms:
10.5 + x = 4.974937186

Solving
10.5 + x = 4.974937186

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 4.974937186 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 4.974937186 + -10.5
x = 4.974937186 + -10.5

Combine like terms: 4.974937186 + -10.5 = -5.525062814
x = -5.525062814

Simplifying
x = -5.525062814

Subproblem 2
x + 10.5 = -4.974937186

Simplifying
x + 10.5 = -4.974937186

Reorder the terms:
10.5 + x = -4.974937186

Solving
10.5 + x = -4.974937186

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -4.974937186 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -4.974937186 + -10.5
x = -4.974937186 + -10.5

Combine like terms: -4.974937186 + -10.5 = -15.474937186
x = -15.474937186

Simplifying
x = -15.474937186

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.525062814, -15.474937186}
Solution
x = {-5.525062814, -15.474937186}