n^2+18n+45=0

Solution for n^2+18n+45=0 equation:

Simplifying
n2 + 18n + 45 = 0

Reorder the terms:
45 + 18n + n2 = 0

Solving
45 + 18n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(15 + n)(3 + n) = 0

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

Simplifying
15 + n = 0

Solving
15 + n = 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 + n = 0 + -15

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

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

Simplifying
n = -15
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

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

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

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

Simplifying
n = -3
Solution
n = {-15, -3}