A concept in supersymmetric quantum mechanics is shape invariant. If two potentials that are related by supersymmetry are shape-invariant, the whole spectrum and the corresponding eigenstates of each Hamiltonian can be solved by simple algebraic means. We investigate a certain method that is used to achieve analytically solvable potentials to the time-independent Schrödinger equation. From such method, a certain condition has to be met for the system to obey unbroken supersymmetry, the kind of supersymmetry that is of usual interest when dealing with shape-invariant potentials. This restriction on the set of analytically solvable potentials that can be achieved using this method helps in identifying which potentials are valid candidates for the test of shape-invariance.