n^2+n-12=170

Solution for n^2+n-12=170 equation:

Simplifying
n2 + n + -12 = 170

Reorder the terms:
-12 + n + n2 = 170

Solving
-12 + n + n2 = 170

Solving for variable 'n'.

Reorder the terms:
-12 + -170 + n + n2 = 170 + -170

Combine like terms: -12 + -170 = -182
-182 + n + n2 = 170 + -170

Combine like terms: 170 + -170 = 0
-182 + n + n2 = 0

Factor a trinomial.
(-14 + -1n)(13 + -1n) = 0

Subproblem 1
Set the factor '(-14 + -1n)' equal to zero and attempt to solve:

Simplifying
-14 + -1n = 0

Solving
-14 + -1n = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1n = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1n = 0 + 14
-1n = 0 + 14

Combine like terms: 0 + 14 = 14
-1n = 14

Divide each side by '-1'.
n = -14

Simplifying
n = -14
Subproblem 2
Set the factor '(13 + -1n)' equal to zero and attempt to solve:

Simplifying
13 + -1n = 0

Solving
13 + -1n = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1n = 0 + -13
-1n = 0 + -13

Combine like terms: 0 + -13 = -13
-1n = -13

Divide each side by '-1'.
n = 13

Simplifying
n = 13
Solution
n = {-14, 13}