Solve for $z$. Assume the equation has a solution for $z$. \[ \begin{array}{l} 16 z+29 z=p z-v \\ z=\square \end{array} \]

Step 1 ：Assume the equation has a solution for z: \(16z + 29z = pz - v\).

Step 2 ：Combine like terms on the left side of the equation to get \(45z = pz - v\).

Step 3 ：Isolate z on one side of the equation to solve for z.

Step 4 ：The solution to the equation is \(z = \boxed{\frac{v}{p-45}}\).