10n^2-2n=0

Solution for 10n^2-2n=0 equation:

Simplifying
10n2 + -2n = 0

Reorder the terms:
-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}