n^2-16n+51=-9

Solution for n^2-16n+51=-9 equation:

Simplifying
n2 + -16n + 51 = -9

Reorder the terms:
51 + -16n + n2 = -9

Solving
51 + -16n + n2 = -9

Solving for variable 'n'.

Reorder the terms:
51 + 9 + -16n + n2 = -9 + 9

Combine like terms: 51 + 9 = 60
60 + -16n + n2 = -9 + 9

Combine like terms: -9 + 9 = 0
60 + -16n + n2 = 0

Factor a trinomial.
(6 + -1n)(10 + -1n) = 0

Subproblem 1
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {6, 10}