Solve using principles of zero products. 6r(7r-6)(6r-1)=0

This is beautiful, because they already gave it to you in factored form.

All you have to do is say to yourself  "This equation is a true statement
when the left side is zero, and the left side is zero whenever ANY ONE
of the factors is zero.". Then jump on it and beat it up.

First factor:
6r = 0
r = 0

Second factor:
7r - 6 = 0
7r = 6
r = 6/7

Third factor:
6r - 1 = 0
6r = 1
r = 1/6