solve the equation (y-1)(y-2)=0

Recall the **Zero-Product Property**, which states that *if the product of two factors is zero then at least one of the factors must be zero*. That is, if a·b=0 then a=0 and/or b=0.

Given: (y - 1)(y - 2) = 0

The equation you are given states that the product of the two factors (y - 1) and (y - 2) is equal to 0. With this, and by the zero-product property, then the factor (y - 1) must be equal o zero and/or the factor (y - 2) must be equal to zero. That is,

** y - 1 = 0 ** and/or **y - 2 = 0**

Solving for y in both cases, we arrive at the following:

y - 1 = 0 ; y - 2 = 0

+ 1 + 1 + 2 + 2

_______________ ________________

y - 1 + 1 = 0 + 1 y - 2 + 2 = 0 + 2

**y = 1** **y = 2**

Thus, the solutions for the equation (y - 1)(y - 2) = 0 are 1 and 2