n(8n+3)=0

Solution for n(8n+3)=0 equation:

Simplifying
n(8n + 3) = 0

Reorder the terms:
n(3 + 8n) = 0
(3 * n + 8n * n) = 0
(3n + 8n2) = 0

Solving
3n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(3 + 8n) = 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 '(3 + 8n)' equal to zero and attempt to solve:

Simplifying
3 + 8n = 0

Solving
3 + 8n = 0

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

Add '-3' to each side of the equation.
3 + -3 + 8n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8n = 0 + -3
8n = 0 + -3

Combine like terms: 0 + -3 = -3
8n = -3

Divide each side by '8'.
n = -0.375

Simplifying
n = -0.375
Solution
n = {0, -0.375}