6r(7r-6)=0

Solution for 6r(7r-6)=0 equation:

Simplifying
6r(7r + -6) = 0

Reorder the terms:
6r(-6 + 7r) = 0
(-6 * 6r + 7r * 6r) = 0
(-36r + 42r2) = 0

Solving
-36r + 42r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6r'.
6r(-6 + 7r) = 0

Ignore the factor 6.
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 '(-6 + 7r)' equal to zero and attempt to solve:

Simplifying
-6 + 7r = 0

Solving
-6 + 7r = 0

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

Add '6' to each side of the equation.
-6 + 6 + 7r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7r = 0 + 6
7r = 0 + 6

Combine like terms: 0 + 6 = 6
7r = 6

Divide each side by '7'.
r = 0.8571428571

Simplifying
r = 0.8571428571
Solution
r = {0, 0.8571428571}