The wires bulged out of my headphone cord. How can I fix this, without solder?
Since that appears to be a coaxial headphone cable, it's unlikely there's a good way to fix the damage shown. If you have special tools, it might be possible to cut completely through the cable, strip appropriately, and crimp the conductors back together, but it isn't practical to buy the tools for a single cable, or for a consumer (and you'll pay more than the headphones are worth to have a professional fix them, which means it's unlikely a pro will have the tool and connector you'd need).
If they're quality over-the-ear phones, it may be worth replacing the entire cable, but otherwise, it will be more cost-effective to replace the complete headphone set.
Someone skilled with a soldering iron may be able to fix this, but the usual method of repair is to replace the entire cable. The headphones will have to be opened up to do that.
If the headphones still work, take electric tape and tape it down to the cable. Worked for me a long time ago. Hope you don't mind a bulge on your cable.
You can crimp the cables and isolate with rubber tape, or in case of "need it right now don't care about tomorrow" you could rip the cables apart some more and manually tie them (always the matching ones of course, color to color). It will look like hell and be not stable. The proper solution would be to replace the cable completely, soldering the end to the speakers. Soldering the broken cable itself will work, but it won't be as flexible at that point anymore.
nevermind, i smashed them with a brick
I think the best way will be either cut the bad part out and then solder wires again without that part or completely replace headphone (I did it!) or cable.