Let x be one of the numbers. Y will be the other for now.

Then since we know xy = 72, we can solve for y, and now think of it as (72/x).

Our other piece of information yields the equation: X + y = -42.

We can only solve for one variable at a time, so we need to write this second equation in terms of just one variable, x:

X + (72/x) = -42.

I like to clear the fractions first, so let's multiply everything on both sides by the LCD, x:

X^2 + 72 = -42x

Then:

X^2 +42x -72 = 0

We would have to use the quadratic formula to solve for x.

This yields two non-integer values for x, and since I'm assuming we need integers, there is no simple solution.

Then since we know xy = 72, we can solve for y, and now think of it as (72/x).

Our other piece of information yields the equation: X + y = -42.

We can only solve for one variable at a time, so we need to write this second equation in terms of just one variable, x:

X + (72/x) = -42.

I like to clear the fractions first, so let's multiply everything on both sides by the LCD, x:

X^2 + 72 = -42x

Then:

X^2 +42x -72 = 0

We would have to use the quadratic formula to solve for x.

This yields two non-integer values for x, and since I'm assuming we need integers, there is no simple solution.