8*n^2-8*n-338=-2

Solution for 8*n^2-8*n-338=-2 equation:

Simplifying
8n2 + -8n + -338 = -2

Reorder the terms:
-338 + -8n + 8n2 = -2

Solving
-338 + -8n + 8n2 = -2

Solving for variable 'n'.

Reorder the terms:
-338 + 2 + -8n + 8n2 = -2 + 2

Combine like terms: -338 + 2 = -336
-336 + -8n + 8n2 = -2 + 2

Combine like terms: -2 + 2 = 0
-336 + -8n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-42 + -1n + n2) = 0

Factor a trinomial.
8((-6 + -1n)(7 + -1n)) = 0

Ignore the factor 8.
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 '(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 = {-6, 7}