8n^2+180=-96n

Solution for 8n^2+180=-96n equation:

Simplifying
8n2 + 180 = -96n

Reorder the terms:
180 + 8n2 = -96n

Solving
180 + 8n2 = -96n

Solving for variable 'n'.

Reorder the terms:
180 + 96n + 8n2 = -96n + 96n

Combine like terms: -96n + 96n = 0
180 + 96n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(45 + 24n + 2n2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(45 + 24n + 2n2)' equal to zero and attempt to solve:

Simplifying
45 + 24n + 2n2 = 0

Solving
45 + 24n + 2n2 = 0

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

Divide each side by '2'.
22.5 + 12n + n2 = 0

Move the constant term to the right:

Add '-22.5' to each side of the equation.
22.5 + 12n + -22.5 + n2 = 0 + -22.5

Reorder the terms:
22.5 + -22.5 + 12n + n2 = 0 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + 12n + n2 = 0 + -22.5
12n + n2 = 0 + -22.5

Combine like terms: 0 + -22.5 = -22.5
12n + n2 = -22.5

The n term is 12n.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12n + 36 + n2 = -22.5 + 36

Reorder the terms:
36 + 12n + n2 = -22.5 + 36

Combine like terms: -22.5 + 36 = 13.5
36 + 12n + n2 = 13.5

Factor a perfect square on the left side:
(n + 6)(n + 6) = 13.5

Calculate the square root of the right side: 3.674234614

Break this problem into two subproblems by setting 
(n + 6) equal to 3.674234614 and -3.674234614.

Subproblem 1
n + 6 = 3.674234614

Simplifying
n + 6 = 3.674234614

Reorder the terms:
6 + n = 3.674234614

Solving
6 + n = 3.674234614

Solving for variable 'n'.

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

Add '-6' to each side of the equation.
6 + -6 + n = 3.674234614 + -6

Combine like terms: 6 + -6 = 0
0 + n = 3.674234614 + -6
n = 3.674234614 + -6

Combine like terms: 3.674234614 + -6 = -2.325765386
n = -2.325765386

Simplifying
n = -2.325765386

Subproblem 2
n + 6 = -3.674234614

Simplifying
n + 6 = -3.674234614

Reorder the terms:
6 + n = -3.674234614

Solving
6 + n = -3.674234614

Solving for variable 'n'.

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

Add '-6' to each side of the equation.
6 + -6 + n = -3.674234614 + -6

Combine like terms: 6 + -6 = 0
0 + n = -3.674234614 + -6
n = -3.674234614 + -6

Combine like terms: -3.674234614 + -6 = -9.674234614
n = -9.674234614

Simplifying
n = -9.674234614

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-2.325765386, -9.674234614}
Solution
n = {-2.325765386, -9.674234614}