10r^2-2r=0

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

Simplifying
10r2 + -2r = 0

Reorder the terms:
-2r + 10r2 = 0

Solving
-2r + 10r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-1 + 5r) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(-1 + 5r)' equal to zero and attempt to solve:

Simplifying
-1 + 5r = 0

Solving
-1 + 5r = 0

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

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

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

Combine like terms: 0 + 1 = 1
5r = 1

Divide each side by '5'.
r = 0.2

Simplifying
r = 0.2
Solution
r = {0, 0.2}