-3 and -20
In order to multiple to a positive number and add to a negative one, both the numbers in question must be negative.
The factors of 60 are:
The third pair listed, 3 and 20, will add up to a positive 23. So all that remains is to make them both negative.
(-20) + (-3) = -23
(-20) * (-3) = 60
83
-397
23
There are no two real numbers that do, but two complex numbers do: (3.5 + i 3.5 √23) and (3.5 - i 3.5 √23) If you want them to add to 7 and multiply to -294, then the two real numbers -14 and 21 work. Or if you want them to add to -7 and multiply to -294, then the two real numbers 14 and -21 work. To add to -7 and multiply to 294, the following two complex numbers work: (-3.5 + i 3.5 √23) and (-3.5 - i 3.5 √23)
53
83
There aren't any whole numbers that satisfy these conditions. The only numbers that multiply to 23 are 23 and 1.
-397
23
73
There are no two real numbers that do, but two complex numbers do: (3.5 + i 3.5 √23) and (3.5 - i 3.5 √23) If you want them to add to 7 and multiply to -294, then the two real numbers -14 and 21 work. Or if you want them to add to -7 and multiply to -294, then the two real numbers 14 and -21 work. To add to -7 and multiply to 294, the following two complex numbers work: (-3.5 + i 3.5 √23) and (-3.5 - i 3.5 √23)
53
-27
45
83
16
113