n^2-6n-31=129

Solution for n^2-6n-31=129 equation:

Simplifying
n2 + -6n + -31 = 129

Reorder the terms:
-31 + -6n + n2 = 129

Solving
-31 + -6n + n2 = 129

Solving for variable 'n'.

Reorder the terms:
-31 + -129 + -6n + n2 = 129 + -129

Combine like terms: -31 + -129 = -160
-160 + -6n + n2 = 129 + -129

Combine like terms: 129 + -129 = 0
-160 + -6n + n2 = 0

Factor a trinomial.
(-10 + -1n)(16 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(16 + -1n)' equal to zero and attempt to solve:

Simplifying
16 + -1n = 0

Solving
16 + -1n = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1n = 0 + -16
-1n = 0 + -16

Combine like terms: 0 + -16 = -16
-1n = -16

Divide each side by '-1'.
n = 16

Simplifying
n = 16
Solution
n = {-10, 16}