6r^2-3r=0

Solution for 6r^2-3r=0 equation:

Simplifying
6r2 + -3r = 0

Reorder the terms:
-3r + 6r2 = 0

Solving
-3r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3r'.
3r(-1 + 2r) = 0

Ignore the factor 3.
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 + 2r)' equal to zero and attempt to solve:

Simplifying
-1 + 2r = 0

Solving
-1 + 2r = 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 + 2r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2r = 0 + 1
2r = 0 + 1

Combine like terms: 0 + 1 = 1
2r = 1

Divide each side by '2'.
r = 0.5

Simplifying
r = 0.5
Solution
r = {0, 0.5}