The Bare X

x(x + 2) = 0: the first factor is x itself, and the rule does not care how plain a factor looks. Either x = 0 or x + 2 = 0. The solutions are 0 and -2.

The forgotten case is always x = 0. It looks too simple to be an answer, so eyes slide past it, but substitute: 0 * (0 + 2) = 0. True, and just as much a solution as the other.

Count factors before you split: a bare x out front is a factor with a vote. Two factors, two cases, two solutions, even when one of them is the humble zero.