n^2+14n-104=-9

Solution for n^2+14n-104=-9 equation:

Simplifying
n2 + 14n + -104 = -9

Reorder the terms:
-104 + 14n + n2 = -9

Solving
-104 + 14n + n2 = -9

Solving for variable 'n'.

Reorder the terms:
-104 + 9 + 14n + n2 = -9 + 9

Combine like terms: -104 + 9 = -95
-95 + 14n + n2 = -9 + 9

Combine like terms: -9 + 9 = 0
-95 + 14n + n2 = 0

Factor a trinomial.
(-19 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-19 + -1n)' equal to zero and attempt to solve:

Simplifying
-19 + -1n = 0

Solving
-19 + -1n = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1n = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1n = 0 + 19
-1n = 0 + 19

Combine like terms: 0 + 19 = 19
-1n = 19

Divide each side by '-1'.
n = -19

Simplifying
n = -19
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-19, 5}