Bring around
Definition 1 of 2
Pro Tip 1/3Change of Heart
Used when someone is convinced to rethink their stance or opinion on an issue. 
After much debate, I was able to bring my friend around to supporting the project.
Pro Tip 2/3Gradual Persuasion
Suggests a process, where convincing occurs over time, not instantly. 
It took weeks, but we finally brought him around to our point of view.
Pro Tip 3/3Positive Connotation
Often implies a constructive or beneficial change in opinion or decision. 
Her speech brought the audience around to understanding the importance of conservation.