The problem was solved. (OK)
The problem was solved by nobody. (Not OK; According to the affirmative verb 'was solved', someone acted out the action, and yet according to the semantic subject, 'nobody', the someone who acted out the action doesn't exist.
Someone solved it.
It was solved (affirmative) by someone.
Nobody solve it.
It wasn't solved (negative) by anyone.
Nobody didn't solve it. (Not OK; Double Negative)
It wasn't solved by nobody. (Not OK; Double negative)
You can't negate the subject (i.e., nobody) to express negation on the verb (i.e., not solve). Verbs and subjects are different animals. They have their own rules.