How do factories and coal/solar/hydro/nuclear plants work?
Factories and the other power plants all give a boost in production to the cities they are built in. In order to build any other power plants, you first need to have a factory built (it gives a 50% boost in your base production). Then, if you have the required technology, you can build one of the power plants (not all 3). They too will give a 50% boost in your base production (before the factory’s bonus); nuclear power plants, however, give a 100% boost (although they can meltdown during civil disorder). Later, you’ll also be able to build a Manufacturing Plant, which gives another 50% bonus on top of a factory and a power plant.