8n^2=16n+384

Solution for 8n^2=16n+384 equation:

Simplifying
8n2 = 16n + 384

Reorder the terms:
8n2 = 384 + 16n

Solving
8n2 = 384 + 16n

Solving for variable 'n'.

Reorder the terms:
-384 + -16n + 8n2 = 384 + 16n + -384 + -16n

Reorder the terms:
-384 + -16n + 8n2 = 384 + -384 + 16n + -16n

Combine like terms: 384 + -384 = 0
-384 + -16n + 8n2 = 0 + 16n + -16n
-384 + -16n + 8n2 = 16n + -16n

Combine like terms: 16n + -16n = 0
-384 + -16n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-48 + -2n + 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}