n^2+3n-180=0

Solution for n^2+3n-180=0 equation:

Simplifying
n2 + 3n + -180 = 0

Reorder the terms:
-180 + 3n + n2 = 0

Solving
-180 + 3n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-15 + -1n)(12 + -1n) = 0

Subproblem 1
Set the factor '(-15 + -1n)' equal to zero and attempt to solve:

Simplifying
-15 + -1n = 0

Solving
-15 + -1n = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1n = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1n = 0 + 15
-1n = 0 + 15

Combine like terms: 0 + 15 = 15
-1n = 15

Divide each side by '-1'.
n = -15

Simplifying
n = -15
Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {-15, 12}