This is the Zero-Product Property: If the result of multiplying two or more numbers is zero, then at least one of the numbers must be zero.
That's all. It sounds so simple. Yet it turns out that this short little rule can do some extremely useful things.
For example, if you know how to solve equations by factoring, then this will look familiar.
Suppose you have to solve an equation involving x2, such as the following:
x2 - 3x = 0.
You can rewrite the left-hand side as a product:
x(x - 3) = 0.
Because of the Zero-Product Property, you know that either x is 0 or x-3 is 0. This means that x is either 0 or 3. Depending on the problem, 0 and 3 might both be correct answers, or one might not fit the context of the problem (it would be called an extraneous solution).
Whenever you come across numbers multiplied together to equal zero, be on the lookout for the Zero-Product Property.