8n^2=-96+64n

Solution for 8n^2=-96+64n equation:

Simplifying
8n2 = -96 + 64n

Solving
8n2 = -96 + 64n

Solving for variable 'n'.

Reorder the terms:
96 + -64n + 8n2 = -96 + 64n + 96 + -64n

Reorder the terms:
96 + -64n + 8n2 = -96 + 96 + 64n + -64n

Combine like terms: -96 + 96 = 0
96 + -64n + 8n2 = 0 + 64n + -64n
96 + -64n + 8n2 = 64n + -64n

Combine like terms: 64n + -64n = 0
96 + -64n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(12 + -8n + n2) = 0

Factor a trinomial.
8((2 + -1n)(6 + -1n)) = 0

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

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