A more modern, category-theory-heavy approach.
: Occasionally, unofficial companion manuals are published that walk through selected problems from major textbooks. Tips for Working Through Solutions solutions to abstract algebra dummit and foote
And if you do find a complete, correct solution to Exercise 18.5.12? Please, for the love of Galois, put it on GitHub. But leave a comment warning about the subtle case. Someone will thank you ten years from now. A more modern, category-theory-heavy approach
If you had to read a solution to understand a problem, close the solution manual. Do not write the answer down immediately. Wait 24 hours, and then attempt to write out the full, rigorous proof from scratch without looking at the manual. If you can do it, you have genuinely learned the concept. Core Areas Where Solutions are Most Valuable Please, for the love of Galois, put it on GitHub