n^2+n-6=50

Solution for n^2+n-6=50 equation:

Simplifying
n2 + n + -6 = 50

Reorder the terms:
-6 + n + n2 = 50

Solving
-6 + n + n2 = 50

Solving for variable 'n'.

Reorder the terms:
-6 + -50 + n + n2 = 50 + -50

Combine like terms: -6 + -50 = -56
-56 + n + n2 = 50 + -50

Combine like terms: 50 + -50 = 0
-56 + n + n2 = 0

Factor a trinomial.
(-8 + -1n)(7 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-8, 7}