If you were told that 7x = 0, you would know that x must be 0. This is because the only way to make the product of two or more numbers equal 0 is to have at least one of those numbers equal 0. Clearly, 7 does not equal 0, which means that x must be 0.
What if you were told that kj = 0? Well, now you have two possibilities. If k = 0, then 0(j) = 0, which is true, so k = 0 is a solution to the equation kj = 0. Likewise, if j = 0, then k(0) = 0, which is also true, so j = 0 is also a solution to kj = 0.
Either of these scenarios make the equation true, and are the only scenarios, in fact, that make the product kj = 0. (If this is not clear, try plugging in non-zero numbers for both k and j and see what happens.)
This is why you want to rewrite quadratic equations such as x2 + 3x − 10 = 0 in factored form: (x + 5)(x − 2) = 0. The left side of the factored equation is a product, so it’s really the same thing as jk = 0. Now you know that either x + 5 is 0, or x − 2 is 0. This means either x = −5 or x = 2. Once you’ve factored a quadratic equation, it’s straightforward to find the solutions.
List all possible solutions to the following equations.
(x − 2)(x − 1) = 0
(x + 4)(x + 5) = 0
(y − 3)(y + 6) = 0