It's already solved, technically speaking. There are several companies already producing green steel, which only make about 5% of the greenhouse gases in production. So the question comes down to cost, not feasibility. Currently green steel costs about 20-30% more than traditional steel. Given these are really just pilot plants and the cost isn't orders of magnitude more expensive, it's not unreasonable to expect green steel to become price-competitive in a few decades. Some (few) companies will wear the extra cost for PR reasons, but it's a hard sell right now. Edit: There may be carbon offsetting options available in some cases to account for the extra cost, so these green steel companies may already be somewhat cost-competitive.