n^2+n-6=234

Solution for n^2+n-6=234 equation:

Simplifying
n2 + n + -6 = 234

Reorder the terms:
-6 + n + n2 = 234

Solving
-6 + n + n2 = 234

Solving for variable 'n'.

Reorder the terms:
-6 + -234 + n + n2 = 234 + -234

Combine like terms: -6 + -234 = -240
-240 + n + n2 = 234 + -234

Combine like terms: 234 + -234 = 0
-240 + n + n2 = 0

Factor a trinomial.
(-16 + -1n)(15 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(15 + -1n)' equal to zero and attempt to solve:

Simplifying
15 + -1n = 0

Solving
15 + -1n = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1n = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1n = 0 + -15
-1n = 0 + -15

Combine like terms: 0 + -15 = -15
-1n = -15

Divide each side by '-1'.
n = 15

Simplifying
n = 15
Solution
n = {-16, 15}