5n^2+15n-360=0

Solution for 5n^2+15n-360=0 equation:

Simplifying
5n2 + 15n + -360 = 0

Reorder the terms:
-360 + 15n + 5n2 = 0

Solving
-360 + 15n + 5n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-72 + 3n + n2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-72 + 3n + n2)' equal to zero and attempt to solve:

Simplifying
-72 + 3n + n2 = 0

Solving
-72 + 3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 3n + 72 + n2 = 0 + 72

Reorder the terms:
-72 + 72 + 3n + n2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 3n + n2 = 0 + 72
3n + n2 = 0 + 72

Combine like terms: 0 + 72 = 72
3n + n2 = 72

The n term is 3n.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3n + 2.25 + n2 = 72 + 2.25

Reorder the terms:
2.25 + 3n + n2 = 72 + 2.25

Combine like terms: 72 + 2.25 = 74.25
2.25 + 3n + n2 = 74.25

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = 74.25

Calculate the square root of the right side: 8.61684397

Break this problem into two subproblems by setting 
(n + 1.5) equal to 8.61684397 and -8.61684397.

Subproblem 1
n + 1.5 = 8.61684397

Simplifying
n + 1.5 = 8.61684397

Reorder the terms:
1.5 + n = 8.61684397

Solving
1.5 + n = 8.61684397

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = 8.61684397 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = 8.61684397 + -1.5
n = 8.61684397 + -1.5

Combine like terms: 8.61684397 + -1.5 = 7.11684397
n = 7.11684397

Simplifying
n = 7.11684397

Subproblem 2
n + 1.5 = -8.61684397

Simplifying
n + 1.5 = -8.61684397

Reorder the terms:
1.5 + n = -8.61684397

Solving
1.5 + n = -8.61684397

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = -8.61684397 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = -8.61684397 + -1.5
n = -8.61684397 + -1.5

Combine like terms: -8.61684397 + -1.5 = -10.11684397
n = -10.11684397

Simplifying
n = -10.11684397

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.11684397, -10.11684397}
Solution
n = {7.11684397, -10.11684397}