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