The phrase "dispose of a problem" is correct and usable in written English.
You could use it in any context in which you are talking about resolving or dealing with a problem. For example: "We quickly had to devise a plan to dispose of the problem before it got worse."
This interstellar ichthyoid neatly disposed of a problem all science-fiction authors have: how to let alien species talk to one another.
Defying the conventional wisdom that mathematics was a young man's game, Erdős went on proving and conjecturing until the age of 83, succumbing to a heart attack only hours after disposing of a nettlesome problem in geometry at a conference in Warsaw.
Expectations of those considering knee OA an occasional problem are mainly symptom relief, whereas expectations of those considering knee OA a chronic problem are to dispose of a treatment being able to modify or stop OA evolution.
How do I dispose of a body?
One may ask, why dispose of a centralized clock?
It would save New York City millions of dollars when one of our three citywide candidates fails to garner 40 percent of a primary vote, and dispose of the problem of slow vote counting by the Board of Elections.
Always dispose of an American flag properly.
If these hale, financially-secure professionals encounter a bag left unattended or a homeless person, they immediately inform the NYPD via Bluetooth, and the cops silently appear as if melting out of the walls and dispose of the problem.
With derivatives, under both its current and proposed authority, the FDIC only has until 5 p.m. on the business day following its appointment as a receiver to dispose of the problems.
That could dispose of the waste problem, reducing the threat of radiation and nuclear proliferation, and at the same time generate vast amounts of low-carbon energy.
