(5n)(n-1)=0

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

Simplifying
(5n)(n + -1) = 0

Remove parenthesis around (5n)
5n(n + -1) = 0

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

Solving
-5n + 5n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5n'.
5n(-1 + n) = 0

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

Simplifying
-1 + n = 0

Solving
-1 + n = 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 + n = 0 + 1

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

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

Simplifying
n = 1
Solution
n = {0, 1}