n^2-14n-51=0

Solution for n^2-14n-51=0 equation:

Simplifying
n2 + -14n + -51 = 0

Reorder the terms:
-51 + -14n + n2 = 0

Solving
-51 + -14n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -1n)(17 + -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 '(17 + -1n)' equal to zero and attempt to solve:

Simplifying
17 + -1n = 0

Solving
17 + -1n = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1n = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1n = 0 + -17
-1n = 0 + -17

Combine like terms: 0 + -17 = -17
-1n = -17

Divide each side by '-1'.
n = 17

Simplifying
n = 17
Solution
n = {-3, 17}