How do you take apart equation rp-21 headphones?

Take off the ear pad. Remove three screws holding the driver mounting, once that's off remove three screws holding the black cap on the back of the earpiece (the part with "Equation " on it). The speaker wires are fed in though a lug on each ear piece so you'll have to unsolder a wire depending on whether you're repairing the left of right earpiece. Remove all screws from the three black plastic housings on each side. Be careful, there is a spring and a small plastic plate under the main swivel joint. Once you have the housings removed you'll see a plastic cap piece under each "leg" going to the earpieces, remove that and you'll see the wire channel.

Make any wiring repair necessary and re assemble. As with any headphone wiring the resin will need to be scraped off the wire before soldering is possible. The ear pad stretches over the earpiece and the thin rubber rim slots into the edge of the earpiece.

The most common fault with these is plastic breakage somewhere in the swivel assembly.