To see how many solutions there are in an equation, it can be determined from the value of the unknown. If the unknown has power to a value, it may have over one solution.
However, in this equation, the unknown has no power, we can thus determine that it has only one solution unless it is not solvable or an math error appears.
To prove the number of solutions this equation have, we can solve the equation:
3z+9+14z=4z+5
Put the unknowns in one side:
3z+14z-4z=5-9
13z=-4
z= -4/13
As z=-4/13, there is only 1 solution for this equation.
Hope it helps!