384=n^2+8n

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

Simplifying
384 = n2 + 8n

Reorder the terms:
384 = 8n + n2

Solving
384 = 8n + n2

Solving for variable 'n'.

Reorder the terms:
384 + -8n + -1n2 = 8n + -8n + n2 + -1n2

Combine like terms: 8n + -8n = 0
384 + -8n + -1n2 = 0 + n2 + -1n2
384 + -8n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
384 + -8n + -1n2 = 0

Factor a trinomial.
(16 + -1n)(24 + n) = 0

Subproblem 1
Set the factor '(16 + -1n)' equal to zero and attempt to solve:

Simplifying
16 + -1n = 0

Solving
16 + -1n = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1n = 0 + -16
-1n = 0 + -16

Combine like terms: 0 + -16 = -16
-1n = -16

Divide each side by '-1'.
n = 16

Simplifying
n = 16
Subproblem 2
Set the factor '(24 + n)' equal to zero and attempt to solve:

Simplifying
24 + n = 0

Solving
24 + n = 0

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

Add '-24' to each side of the equation.
24 + -24 + n = 0 + -24

Combine like terms: 24 + -24 = 0
0 + n = 0 + -24
n = 0 + -24

Combine like terms: 0 + -24 = -24
n = -24

Simplifying
n = -24
Solution
n = {16, -24}