The way to solve these types of questions is get the variable you are trying to solve for, which in this case is 'z', and get it to one side of the equation, usually the left hand side, and the result of the equation or the solution onto the opposite side, typically the right hand side.
First things off, we can combine like terms on the left hand side since both terms are 'z' multiples.
16z + 29z = pz - v
45z = pz - v
Next, I want to get all 'z' like terms on one side of the equation. We can accomplish this by subtracting "pz" from both sides.
45z - pz = pz - v - pz
After completing the subtraction we get:
45z - pz = -v
Next, factor out the 'z' from the left hand side:
z(45 - p) = -v
And finally, divide both sides by (45 - p)
z = -v / (45 - p)
