start by simplifying the equation by cross multiplying
9(z+1) = 3z
then distribute 9 into the brackets
9z + 9= 3z
then move the constant to the right hand side and change its sign
9z = 3z -9
then move the variable to the left hand side and change its sign
9z - 3z = -9
collect like terms
6z = - 9
then divide both equations by 6 to get z by itself
z = -9/6
simplify the fraction
z = -3/2
