n^2+n-6=126

Solution for n^2+n-6=126 equation:

Simplifying
n2 + n + -6 = 126

Reorder the terms:
-6 + n + n2 = 126

Solving
-6 + n + n2 = 126

Solving for variable 'n'.

Reorder the terms:
-6 + -126 + n + n2 = 126 + -126

Combine like terms: -6 + -126 = -132
-132 + n + n2 = 126 + -126

Combine like terms: 126 + -126 = 0
-132 + n + n2 = 0

Factor a trinomial.
(-12 + -1n)(11 + -1n) = 0

Subproblem 1
Set the factor '(-12 + -1n)' equal to zero and attempt to solve:

Simplifying
-12 + -1n = 0

Solving
-12 + -1n = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1n = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1n = 0 + 12
-1n = 0 + 12

Combine like terms: 0 + 12 = 12
-1n = 12

Divide each side by '-1'.
n = -12

Simplifying
n = -12
Subproblem 2
Set the factor '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Solution
n = {-12, 11}