What are the zeros of the quadratic equation whose leading coefficient is -1 and coefficient of x is -7 and constant term is -12?

In other Words, the zeroes of -x2 - 7x - 12.

First, multiply by -1: x2 + 7x + 12.

The new leading coefficient is 1, so the factors take the form (x + _)(x + _), where the two blanked-out numbers add up to 7 and multiply to 12.

It's easier to try factoring 12 and adding the factors:

1 + 12 = 13

2 + 6 = 8

3 + 4 = 7

That last one shows us that the factors are (x + 3)(x + 4), and the zeroes are -3 and -4.