  We study the null and time-like geodesics of the light and the neutral
particles respectively in the exterior of Kerr-Newman black holes. The geodesic
equations are known to be written as a set of first-order differential
equations in Mino time from which the angular and radial potentials can be
defined. We classify the roots for both potentials, and mainly focus on those
of the radial potential with an emphasis on the effect from the charge of the
black holes. We then obtain the solutions of the trajectories in terms of the
elliptical integrals and the Jacobian elliptic functions for both null and
time-like geodesics, which are manifestly real functions of the Mino time that
the initial conditions can be explicitly specified. We also describe the
details of how to reduce those solutions into the cases of the spherical
orbits. The effect of the black hole's charge decreases the radii of the
spherical motion of the light and the particle for both direct and retrograde
motions. In particular, we focus on the light/particle boomerang of the
spherical orbits due to the frame dragging from the back hole's spin with the
effect from the charge of the black hole. To sustain the change of the
azimuthal angle of the light rays, say for example $\Delta \phi=\pi$ during the
whole trip, the presence of the black hole's charge decreases the radius of the
orbit and consequently reduces the needed values of the black hole's spin. As
for the particle boomerang, the particle's inertia renders smaller change of
the angle $\Delta \phi$ as compared with the light boomerang. Moreover, the
black hole's charge also results in the smaller angle change $\Delta \phi$ of
the particle than that in the Kerr case. The implications of the obtained
results to observations are discussed.
