(n+9)(2n-4)=180

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

Simplifying
(n + 9)(2n + -4) = 180

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

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

Multiply (9 + n) * (-4 + 2n)
(9(-4 + 2n) + n(-4 + 2n)) = 180
((-4 * 9 + 2n * 9) + n(-4 + 2n)) = 180
((-36 + 18n) + n(-4 + 2n)) = 180
(-36 + 18n + (-4 * n + 2n * n)) = 180
(-36 + 18n + (-4n + 2n2)) = 180

Combine like terms: 18n + -4n = 14n
(-36 + 14n + 2n2) = 180

Solving
-36 + 14n + 2n2 = 180

Solving for variable 'n'.

Reorder the terms:
-36 + -180 + 14n + 2n2 = 180 + -180

Combine like terms: -36 + -180 = -216
-216 + 14n + 2n2 = 180 + -180

Combine like terms: 180 + -180 = 0
-216 + 14n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-108 + 7n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-108 + 7n + n2)' equal to zero and attempt to solve:

Simplifying
-108 + 7n + n2 = 0

Solving
-108 + 7n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '108' to each side of the equation.
-108 + 7n + 108 + n2 = 0 + 108

Reorder the terms:
-108 + 108 + 7n + n2 = 0 + 108

Combine like terms: -108 + 108 = 0
0 + 7n + n2 = 0 + 108
7n + n2 = 0 + 108

Combine like terms: 0 + 108 = 108
7n + n2 = 108

The n term is 7n.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7n + 12.25 + n2 = 108 + 12.25

Reorder the terms:
12.25 + 7n + n2 = 108 + 12.25

Combine like terms: 108 + 12.25 = 120.25
12.25 + 7n + n2 = 120.25

Factor a perfect square on the left side:
(n + 3.5)(n + 3.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(n + 3.5) equal to 10.9658561 and -10.9658561.

Subproblem 1
n + 3.5 = 10.9658561

Simplifying
n + 3.5 = 10.9658561

Reorder the terms:
3.5 + n = 10.9658561

Solving
3.5 + n = 10.9658561

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = 10.9658561 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = 10.9658561 + -3.5
n = 10.9658561 + -3.5

Combine like terms: 10.9658561 + -3.5 = 7.4658561
n = 7.4658561

Simplifying
n = 7.4658561

Subproblem 2
n + 3.5 = -10.9658561

Simplifying
n + 3.5 = -10.9658561

Reorder the terms:
3.5 + n = -10.9658561

Solving
3.5 + n = -10.9658561

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = -10.9658561 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = -10.9658561 + -3.5
n = -10.9658561 + -3.5

Combine like terms: -10.9658561 + -3.5 = -14.4658561
n = -14.4658561

Simplifying
n = -14.4658561

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.4658561, -14.4658561}
Solution
n = {7.4658561, -14.4658561}