A new variational method is proposed to solve the three-fermion problem, in which two of the particles have the same mass. We obtain the total energy of the system for all masses in two and three spatial dimensions. In this way we can calculate the energies and wavefunctions of a wide range of systems including , the charged exciton, and many others, in a unified manner. The scaling properties of total energy, wavefunction, and effective potential are derived and the relevant scaling parameters are introduced.