10r^2-6r=0

Solution for 10r^2-6r=0 equation:

Simplifying
10r2 + -6r = 0

Reorder the terms:
-6r + 10r2 = 0

Solving
-6r + 10r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-3 + 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 '(-3 + 5r)' equal to zero and attempt to solve:

Simplifying
-3 + 5r = 0

Solving
-3 + 5r = 0

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

Add '3' to each side of the equation.
-3 + 3 + 5r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 5r = 0 + 3
5r = 0 + 3

Combine like terms: 0 + 3 = 3
5r = 3

Divide each side by '5'.
r = 0.6

Simplifying
r = 0.6
Solution
r = {0, 0.6}