What two numbers, if added together, would equal - 15 but when multiplied together would equal - 42

Consider factors of 42, then if the factors can be added or subtracted.

42 = 42 * 1

42 = 21 * 2

42 = 14 * 3

42 = 7 * 6

Since none of these can be added or subtracted to equal 15, no intergers satisfy these criteria.