завое(вы)вать любовь

2. фраз. to gain favo(u)r with smb

Maxim could not understand the economic reasons for this popularity, but apparently it was related to their tactics: the military clique curbed the appetites of the industrialists, thereby gaining favor with the workers.

2. фраз. to gain acceptance

One theory regarding the extinction of dinosaurs which is gaining some acceptance is that because they were warm-blooded creatures with a high metabolism, they were more susceptible to viruses or bacterial infections than their cold-blooded predecessors.