n^2+20n+75=0

Solution for n^2+20n+75=0 equation:

Simplifying
n2 + 20n + 75 = 0

Reorder the terms:
75 + 20n + n2 = 0

Solving
75 + 20n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(15 + n)(5 + 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 '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Solution
n = {-15, -5}