How can I solve for z? 3+sqrt(z-6)=sqrt(z+9)
The general rule is to isolate the square root, then square both sides. In your problem we need to do this twice.
One square root is already isolated, so square both sides:
Now isolate the square root:
And square both sides.
Always always always when you get a final answer for z make sure it is a solution to the original equation. Extra solutions tend to come out that don't satisfy the original equation.