n(5n+1)=0

Solution for n(5n+1)=0 equation:

Simplifying
n(5n + 1) = 0

Reorder the terms:
n(1 + 5n) = 0
(1 * n + 5n * n) = 0
(1n + 5n2) = 0

Solving
1n + 5n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(1 + 5n) = 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 '(1 + 5n)' equal to zero and attempt to solve:

Simplifying
1 + 5n = 0

Solving
1 + 5n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5n = 0 + -1
5n = 0 + -1

Combine like terms: 0 + -1 = -1
5n = -1

Divide each side by '5'.
n = -0.2

Simplifying
n = -0.2
Solution
n = {0, -0.2}