8n^2=-384+112n

Solution for 8n^2=-384+112n equation:

Simplifying
8n2 = -384 + 112n

Solving
8n2 = -384 + 112n

Solving for variable 'n'.

Reorder the terms:
384 + -112n + 8n2 = -384 + 112n + 384 + -112n

Reorder the terms:
384 + -112n + 8n2 = -384 + 384 + 112n + -112n

Combine like terms: -384 + 384 = 0
384 + -112n + 8n2 = 0 + 112n + -112n
384 + -112n + 8n2 = 112n + -112n

Combine like terms: 112n + -112n = 0
384 + -112n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(48 + -14n + n2) = 0

Factor a trinomial.
8((6 + -1n)(8 + -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 '(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
Solution
n = {6, 8}