Hi Phoenix, it is possible, there are many adult swim classes around. If I can learn to swim anyone can. I have not coordination at all.
The trickiest part for me was learning to not fear putting my face in the water, and then blowing bubbles out of my nose to breath in water. I had a few lessons, and the most helpful thing was learning to roll onto my back and trusting that I could float like that if I got tired.
I practiced a lot, in shallow water before I was confident enough to venture into the deep.