-n(10n+2)=0

Solution for -n(10n+2)=0 equation:

Simplifying
-1n(10n + 2) = 0

Reorder the terms:
-1n(2 + 10n) = 0
(2 * -1n + 10n * -1n) = 0
(-2n + -10n2) = 0

Solving
-2n + -10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-2n'.
-2n(1 + 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 '(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}