n(10n+8)=0

Solution for n(10n+8)=0 equation:

Simplifying
n(10n + 8) = 0

Reorder the terms:
n(8 + 10n) = 0
(8 * n + 10n * n) = 0
(8n + 10n2) = 0

Solving
8n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n'.
2n(4 + 5n) = 0

Ignore the factor 2.
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 '(4 + 5n)' equal to zero and attempt to solve:

Simplifying
4 + 5n = 0

Solving
4 + 5n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5n = 0 + -4
5n = 0 + -4

Combine like terms: 0 + -4 = -4
5n = -4

Divide each side by '5'.
n = -0.8

Simplifying
n = -0.8
Solution
n = {0, -0.8}