n^2+19n+66=6

Solution for n^2+19n+66=6 equation:

Simplifying
n2 + 19n + 66 = 6

Reorder the terms:
66 + 19n + n2 = 6

Solving
66 + 19n + n2 = 6

Solving for variable 'n'.

Reorder the terms:
66 + -6 + 19n + n2 = 6 + -6

Combine like terms: 66 + -6 = 60
60 + 19n + n2 = 6 + -6

Combine like terms: 6 + -6 = 0
60 + 19n + n2 = 0

Factor a trinomial.
(15 + n)(4 + 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 '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Solution
n = {-15, -4}