The solutions are x = 1 and x = 2. To see this, factor x² - 3x + 2 as (x - 1)(x - 2). The equation then says that

(x - 1)(x - 2) = 0

But if a product of two numbers is zero, at least one of those numbers is zero. In other words, either

(x - 1) = 0     or     (x - 2) = 0.

In the first case, we get x = 1. In the second case, we get x = 2.

Thus, the two solutions are

x = 1 and x = 2.

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