What are two numbers that multiply to get - 64, but when added get 0?

The simplest way in solving this is to find the factors of 64, and its corresponding negative values.

So, x = {1, 2, 4, 8, 16, 32, 64}

So its corresponding x values to get - 64 are:

x = {-64, - 32, - 16, - 8, - 4, - 2, - 1}

Now, we notice that 8 and - 8 are the same magnitude, with opposite signs. That means when they are added, they will cancel.

Hence, your two numbers are 8 and - 8