Oh yes, working out at home is definitely possible but we need a strong motivation to workout from home.
I have tried it and succeeded to some extent but honestly speaking, I prefer hitting the gym.
Calisthenic exercises like Pushup, situp, hollow body holds can be done without any equipment. Only pull ups require a pull up bar which you can order online as well.
These are good if done in the proper form. Form is of utmost importance or else the muscles dont get activated and you will not see any changes over the years.
But these calisthenics are the oldest form of free hand exercise and they are difficult to master, much better than going to a gym and getting into that subculture, I dont like it anyway.