(2x+4)(2x+9)=180

Solution for (2x+4)(2x+9)=180 equation:

Simplifying
(2x + 4)(2x + 9) = 180

Reorder the terms:
(4 + 2x)(2x + 9) = 180

Reorder the terms:
(4 + 2x)(9 + 2x) = 180

Multiply (4 + 2x) * (9 + 2x)
(4(9 + 2x) + 2x * (9 + 2x)) = 180
((9 * 4 + 2x * 4) + 2x * (9 + 2x)) = 180
((36 + 8x) + 2x * (9 + 2x)) = 180
(36 + 8x + (9 * 2x + 2x * 2x)) = 180
(36 + 8x + (18x + 4x2)) = 180

Combine like terms: 8x + 18x = 26x
(36 + 26x + 4x2) = 180

Solving
36 + 26x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
36 + -180 + 26x + 4x2 = 180 + -180

Combine like terms: 36 + -180 = -144
-144 + 26x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-144 + 26x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + 13x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-72 + 13x + 2x2)' equal to zero and attempt to solve:

Simplifying
-72 + 13x + 2x2 = 0

Solving
-72 + 13x + 2x2 = 0

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

Divide each side by '2'.
-36 + 6.5x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 6.5x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 6.5x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 6.5x + x2 = 0 + 36
6.5x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
6.5x + x2 = 36

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = 36 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 36 + 10.5625

Combine like terms: 36 + 10.5625 = 46.5625
10.5625 + 6.5x + x2 = 46.5625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 46.5625

Calculate the square root of the right side: 6.823672032

Break this problem into two subproblems by setting 
(x + 3.25) equal to 6.823672032 and -6.823672032.

Subproblem 1
x + 3.25 = 6.823672032

Simplifying
x + 3.25 = 6.823672032

Reorder the terms:
3.25 + x = 6.823672032

Solving
3.25 + x = 6.823672032

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 6.823672032 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 6.823672032 + -3.25
x = 6.823672032 + -3.25

Combine like terms: 6.823672032 + -3.25 = 3.573672032
x = 3.573672032

Simplifying
x = 3.573672032

Subproblem 2
x + 3.25 = -6.823672032

Simplifying
x + 3.25 = -6.823672032

Reorder the terms:
3.25 + x = -6.823672032

Solving
3.25 + x = -6.823672032

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -6.823672032 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -6.823672032 + -3.25
x = -6.823672032 + -3.25

Combine like terms: -6.823672032 + -3.25 = -10.073672032
x = -10.073672032

Simplifying
x = -10.073672032

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.573672032, -10.073672032}
Solution
x = {3.573672032, -10.073672032}