n^2-6n-64=8

Solution for n^2-6n-64=8 equation:

Simplifying
n2 + -6n + -64 = 8

Reorder the terms:
-64 + -6n + n2 = 8

Solving
-64 + -6n + n2 = 8

Solving for variable 'n'.

Reorder the terms:
-64 + -8 + -6n + n2 = 8 + -8

Combine like terms: -64 + -8 = -72
-72 + -6n + n2 = 8 + -8

Combine like terms: 8 + -8 = 0
-72 + -6n + n2 = 0

Factor a trinomial.
(-6 + -1n)(12 + -1n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
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
Solution
n = {-6, 12}