n^2-16n-51=6

Solution for n^2-16n-51=6 equation:

Simplifying
n2 + -16n + -51 = 6

Reorder the terms:
-51 + -16n + n2 = 6

Solving
-51 + -16n + n2 = 6

Solving for variable 'n'.

Reorder the terms:
-51 + -6 + -16n + n2 = 6 + -6

Combine like terms: -51 + -6 = -57
-57 + -16n + n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-57 + -16n + n2 = 0

Factor a trinomial.
(-3 + -1n)(19 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 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 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
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
Solution
n = {-3, 19}