Think Order of Operations, PEMDAS, parentheses, exponents, multiply and divide, add and subtract.
First you have to distribute the 5 on the left side and the 9 on the left side to each term in the corresponding parentheses.
5(2z-3)=9(z-3)
5*2z-5*3 = 9*z-9*3
10z-15 = 9z-27
then add 15 to both sides
10z=9z-12
then subtract 9z from both sides
z=-12
that's your answer! Just go through the order of operations and remember whatever you do to one side of the equation you must do to the other.