What is the movie "a clockwork orange" about?

Ok, so this is kind of a spoiler, just warning, but this is what it's about: "Alex (Malcolm McDowell) is a cheerful young man who enjoys , violence, clical music, and just about everything sadistic. With his three droogs, Alex spends the nights terrorizing anyone who he might encounter. One night, after killing a woman with numerous cats, Alex's gang turns on him and leaves him at the hands of the law. Alex next finds himself in prison with the sentence of 14 years for his murder that night. While in prison, he hears about a free ticket out of his sentence. All he has to do is be a guinea pig for a scientific experiment. The experiment is supposed to make Alex "better" and revert him from being bad to good. Alex says yes, jumping at the opportunity to get free faster. After being brainwashed by the scientists, Alex returns to civilization as a free and good man. However, the experiment has some side-effects that were not intended, and Alex is left helpless as his past victims come to gain revenge on him."