  In this paper we have added Maxwell, Maxwell-Chern-Simons and gravitational
Chern-Simons terms to Born-Infeld extended new massive gravity and we have
found different types of (non)extremal charged black holes. For each black hole
we find mass, angular momentum, entropy and temperature. Since our solutions
are asymptotically AdS or warped-AdS, we infer central charges of dual CFTs by
using Cardy's formula. Computing conserved charges associated to asymptotic
symmetry transformations confirms calculation of central charges. For CFTs dual
to asymptotically AdS solutions we find left central charges from Cardy's
formula, while conserved charge approach gives both left and right central
charges. For CFTs dual to asymptotically warped-AdS solutions, left and right
central charges are equal when we have Maxwell-Chern-Simons term but they have
different values when gravitational Chern-Simons term is included.
