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To solve this problem, we can set up a system of equations. Let's call the two numbers x and y. We know that xy = 32 and x + y = -12. By substituting the value of y from the second equation into the first equation, we get x(-12-x) = 32. Simplifying this equation, we get -12x - x^2 = 32. Rearranging the terms, we get x^2 + 12x - 32 = 0. By factoring or using the quadratic formula, we find the solutions x = -8 and x = 4. Therefore, the two numbers are -8 and -4.
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