We provide a unified treatment of the two distinct states of vertically thin AGN accretion disks: a cool (T approximately 10(6) K) optically thick solution, and a hot (T(e) approximately 10(9) K, optically thin solution. We introduce a generalized formalism and a new radiative cooling equation valid in both regimes. We find a new luminosity limit L < L(E) at which the hot and cool alpha-solutions merge into a single solution of intermediate optical depth. For the hot solutions we consider four cases: different ion and electron temperatures or ions and electrons in thermal equilibrium, with Comptonized bremsstrahlung or unsaturated Compton cooling. Analytic solutions for the disk structure are given, and output spectra are computed numerically. This is used to demonstrate the prospect of fitting AGN broad-band spectra, containing both the UV bump as well as hard X-ray and gamma-ray tail, using a single accretion disk model. Such models make definite predictions on the observed spectrum, such as the relation between the hard X-ray spectral index, the UV-to-X-ray luminosity ratio, and a approximately 1 MeV feature.