n^2+12n-77=8

Solution for n^2+12n-77=8 equation:

Simplifying
n2 + 12n + -77 = 8

Reorder the terms:
-77 + 12n + n2 = 8

Solving
-77 + 12n + n2 = 8

Solving for variable 'n'.

Reorder the terms:
-77 + -8 + 12n + n2 = 8 + -8

Combine like terms: -77 + -8 = -85
-85 + 12n + n2 = 8 + -8

Combine like terms: 8 + -8 = 0
-85 + 12n + n2 = 0

Factor a trinomial.
(-17 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-17 + -1n)' equal to zero and attempt to solve:

Simplifying
-17 + -1n = 0

Solving
-17 + -1n = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1n = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1n = 0 + 17
-1n = 0 + 17

Combine like terms: 0 + 17 = 17
-1n = 17

Divide each side by '-1'.
n = -17

Simplifying
n = -17
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-17, 5}