I am trying to fix headphones and I am not sure how to reconnect them,
My question is can i just connect them as they are and solder the ends together, or do I have to uncoil each (colored) individual wire and connect the smaller wires together, the ones that make up the colored wire, like in this picture below
Also, what is isolating the wires so that the electricity from the red one does not flow trough the green one? Im not sure what that is called.
Any help is appreciated, thank you.

My question is can i just connect them as they are and solder the ends together, or do I have to uncoil each (colored) individual wire and connect the smaller wires together, the ones that make up the colored wire, like in this picture below

Also, what is isolating the wires so that the electricity from the red one does not flow trough the green one? Im not sure what that is called.
Any help is appreciated, thank you.