3n(2n+8)=n

Solution for 3n(2n+8)=n equation:

Simplifying
3n(2n + 8) = n

Reorder the terms:
3n(8 + 2n) = n
(8 * 3n + 2n * 3n) = n
(24n + 6n2) = n

Solving
24n + 6n2 = n

Solving for variable 'n'.

Reorder the terms:
24n + -1n + 6n2 = n + -1n

Combine like terms: 24n + -1n = 23n
23n + 6n2 = n + -1n

Combine like terms: n + -1n = 0
23n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(23 + 6n) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(23 + 6n)' equal to zero and attempt to solve:

Simplifying
23 + 6n = 0

Solving
23 + 6n = 0

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

Add '-23' to each side of the equation.
23 + -23 + 6n = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 6n = 0 + -23
6n = 0 + -23

Combine like terms: 0 + -23 = -23
6n = -23

Divide each side by '6'.
n = -3.833333333

Simplifying
n = -3.833333333
Solution
n = {0, -3.833333333}