i have to show this equation represents a sphere..
but i'm stuck on the z variable as it won't come down to an even square. it comes down to a (x+2)(x-2).
You apparently are trying to do this as
which is wrong for two reasons. First, moving that "- 4" to the other side of the equation makes it " " which cannot be factored, not " ".
But you don't want to do that to begin with!
Instead leave that constant, 4, on the right and do it as
Complete the square in x and y. The "z" term is already a perfect square! The numbers you need to add on the left to make the perfect squares, and, of course, add on the right, will give you a positive number on the right.