n^2+25n+66=0

Solution for n^2+25n+66=0 equation:

Simplifying
n2 + 25n + 66 = 0

Reorder the terms:
66 + 25n + n2 = 0

Solving
66 + 25n + n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(22 + n)' equal to zero and attempt to solve:

Simplifying
22 + n = 0

Solving
22 + n = 0

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

Add '-22' to each side of the equation.
22 + -22 + n = 0 + -22

Combine like terms: 22 + -22 = 0
0 + n = 0 + -22
n = 0 + -22

Combine like terms: 0 + -22 = -22
n = -22

Simplifying
n = -22
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 = {-22, -3}