Hi Sonya. Richard S. already gave you a nice explanation of how to do this problem. Here are some general things to keep in mind.
When doing an algebra problem where you have to solve for a variable (in your case, z) - remember your goal is to get z alone. It'll usually take several steps to get there. Richard's thought's about "undoing" subtraction by addition, or division by multiplication, is a good way to think about it. Remember though, as you are "undoing" operations, you have to do that in REVERSE PEMDAS order. (PEMDAS = order of operations - Parenthesis first, followed by Exponents, next [Multiplication and Division in the order they appear], and finally [Addition and Subtraction in the order they appear]. That is why Richard is telling you to start with undoing subtraction first.
Don't forget that special rule of mathematics: what you do to one side you do to the other. Always.
As you move things around by "undoing" to get the variable you are solving for (in this case, z) alone, remember it doesn't matter if you move everything but z to the right side of the equation, and wind up with something like z = "blah blah blah" , or if you move everything but z to the left side and wind up with "blah blah blah" = z. Depending on your given equation you might do it one way or the other. I've always found it easier to keep z on whatever side it is on if it is already positive in your equation, or move it to the other side to MAKE it positive if it appears in your equation as a negative. This might save you a sign error at the very end, because you are always solving for positive z.