  We calculate the equation of state at non-zero temperature and density from
first principles in two-, three- and four-color QCD with two fermion flavors in
the fundamental and two-index, antisymmetric representation. By matching
low-energy results (from a `hadron resonance gas') to high-energy results from
(resummed) perturbative QCD, we obtain results for the pressure and trace
anomaly that are in quantitative agreement with full lattice-QCD studies for
three colors at zero chemical potential. Our results for non-zero chemical
potential at zero temperature constitute predictions for the equation of state
in QCD-like theories that can be tested by traditional lattice studies for
two-color QCD with two fundamental fermions and four-color QCD with two
two-index, antisymmetric fermions. We find that the speed of sound squared at
zero temperature can exceed one third, which may be relevant for the
phenomenology of high-mass neutron stars.
