win over
US /wɪn ˈoʊvər/
UK /wɪn ˈoʊvər/

1.
ganarse, convencer
to gain the support, confidence, or approval of someone
:
•
He tried to win over the skeptical audience with his passionate speech.
Intentó ganarse a la audiencia escéptica con su apasionado discurso.
•
It took a lot of effort to win her over to our side.
Costó mucho esfuerzo ganársela para nuestro lado.