'To solve' versus 'To solving'

The infinitive (or perhaps it should be analyzed as the subjunctive?) gives a sense of completion, while the gerund gives more of a sense of process. So "There is a new approach to solving homelessness" indicates that the approach will help work on the problem of homelessness, while "There is a new approach to solve homelessness" implies that it will successfully deal with homelessness. A further complication is that "silver bullet" is a metaphor (or, at least, I hope people aren't discussing literally solving homelessness with silver bullets), and there can be differences as to what people consider it a metaphor for. It's often used as a metaphor for something that completely takes care of something, which suggests the infinitive. If, however, it's used as a metaphor for a tool used in the process of doing something, rather than something that automatically gets one to one's end goal, that suggests the gerund.