How do I make a headphone cable extension?

Please excuse my lack of knowlege of the correct terms, I will try to describe things as best I can.

I am trying to make a 15metre extension cord for my PC speakers (logitech ls21 speakers + subwoofer) so that I can listen to music at the other end of the house, and I am running into some problems.

I have bought male and female headphone plugs. I have also bought the right length of wire (2 thin copper wires in separate conduits, which are joined together). I suspect, however, that this is not the correct sort of wire to use. I don't have a soldering iron, but I suspect I may need one.

Each of the headphone plugs has 2 little metal tags with holes in them, as well as a larger metal tongue with a hole in it. The larger tongue is in a "T" shape, with the arms of the T bent around.

So far, I have tried stripping a small amount of the wire at each end, and connecting one half to each of the smaller metal tags on each of the male and female headphone plugs. This resulted in an awful sound, with some treble missing and no bass from the subwoofer. I quickly turned it off.

Do I need some sort of 3-way cable? I gather that I need an earth wire as well, but in some of the youtube videos I have watched, this is just combined with one of the other wires, which I don't understand at all (if it's just being combined with the wire, why the need for it at all?).

Another way which seems like the easiest for me at this stage is to buy 2 RCA to 3.5mm cable adapters; a male and a female, as well as 2 male and 2 female RCA plugs, and wire each side individually, using twice as much wire.

I would greatly appreciate any advice anyone can give me.