Use the zero product property to find the solutions to the equation x^2+x-30=12

(6, - 7)

Step-by-step explanation:

Rewriting x^2+x-30=12 in standard form for a quadratic equation yields

x^2+x-42 = 0. This, in turn, can be factored: (x+7) (x-6) = 0.

Here the product of these two factors is zero.

Solving x+7=0 for x, we get x = - 7; solving x-6 for x, we get x = 6.

The solutions are {6, - 7).