This does not make type sense, or at least more explanation is needed. What do you mean by the product of two sets: the Cartesian product or maybe ? What does 0 mean: is it a number? Then how can a product of two sets equal a number? Similarly, for what x do you consider f(x)g(x), or is it some product of functions as a whole?f(x).g(x) = A.B = 0 [A product B]
Try to find a relationship between the propositions f(x) = 0 and f(x)g(x) = 0. Which implies which? What does it say about the relationship between A and the solution set of f(x)g(x) = 0?