  We present a complete theory for laser cooling of a macroscopic
radio-frequency LC electrical circuit by means of an optoelectromechanical
system, consisting of an optical cavity dispersively coupled to a
nanomechanical oscillator, which is in turn capacitively coupled to the LC
circuit of interest. We determine the optimal parameter regime where the LC
resonator can be cooled down to its quantum ground state, which requires a
large optomechanical cooperativity, and a larger electromechanical
cooperativity. Moreover, comparable optomechanical and electromechanical
coupling rates are preferable for reaching the quantum ground state.
