My students generally write essays that have at least five paragraphs, often more. I would suggest that you do something like this:
Explain and describe the problem and why this should be solved. End with a question which is asking how the problem can be solved. Example: How can we solve the problem of school shootings?
Then in the next paragraph, you would give your solution idea. If your idea is easy to explain, then you would spend the rest of your paper refuting objections and explaining why your idea would work and be cost-effective, feasible, and effective.
On the other hand, if your idea is complicated to explain, you will need to spend a longer part of your paper making sure the reader understands it. In both cases, you will need to refute any objections and help the reader to see how important it is to do this solution.