In a compromise, each person gives up something such that everyone involved suffers ‘fairly’ and ‘equally’. A genuine solution, on the other hand, is one which everyone involved prefers, including preferring it to their own antecedent preference. No one is suffering, ‘fairly’, ‘equally’ or otherwise.
Does the proposed solution spark joy? Is everyone beaming? Are our eyes all shining? Do you see delight? Joy? Animation? Skipping? The odd cartwheel, perhaps? Is it a “YES!!!!” all round? That suggests you have created a real solution.
We look at our respective reasons for wanting what we initially want, and we create a way to proceed that we all prefer—a new idea that did not exist at the outset.