Solve the following equation. Write your answer in reduced fraction form, if necessary.

The equation can be solved by applying the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero.

So, we have two cases to consider:

Case 1: 6x = 0
Dividing both sides by 6, we get:
x = 0/6
Simplifying, we have:
x = 0

Case 2: (x-1) = 0
Adding 1 to both sides, we have:
x = 1

The solutions to the equation are x = 0 and x = 1.
Therefore, the answer is x = 0, 1.