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(y+15)(y+12)=0

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     (y + 15)(y + 12) = 0

Recall the zero product property, which states that if the product of two factors is equal to zero then one or both factors is equal to zero. Using this property, we can set each factor equal to 0 and solve for y. That is,

     y + 15 = 0          and          y + 12 = 0

Solve for y in each case:

     y + 15 = 0

     y + 15 - 15 = 0 - 15

     y + 0 = -15

     y = -15

and

     y + 12 = 0

     y + 12 - 12 = 0 - 12

     y + 0 = -12

     y = -12

Thus, the two solutions to the equation are:     y = -15     and     y = -12