DO NOT attempt to desolder the white shrink wrapped wire located at the bottom left of the trigger assembly. It requires advanced soldering techniques and isn't necessary.

The soldering iron is hot and could burn you.

Take note of where each wire is attached to the trigger assembly for resoldering the new trigger.

Use the soldering iron to desolder and remove the red, blue, and three black wires.

If you don't know how to desolder, or need to brush up on your skills, iFixit posted a How To Solder and Desolder Connections guide.