possible girlfriend is sceptical about relationship

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sup /adv/
i need some help with this girl i like and i'd like to say i'm pretty close to being in a relationship with her, but she's been in some shitty relationships and none of her family members are in relationships like her Mum/Dad, Nan/Pop etc haven't been together since she was a kid and her previous boyfriend cheated on her on more than one occasion and now she's worried that i might cheat on her if we get too close and she understandably has some trust issues with that kinda stuff.

i haven't had a girlfriend before but I've had crushes and stuff on girls in the past that never went anywhere because all of them were pretty one sided and most of these were on the height of my depression(mid teens) so i'd ask them out after maybe 4-5 weeks and because of that she's nervous that if i talk to other women that i'll fall for them and cheat/leave her for them.

i need some help (or if you would /adv/ice in) convincing her that i won't do this but of course she wont believe me because of all that I've mentioned above. she's just worried and i'm not sure what i should say to help prove that 'm good for her and wont hurt her.

I'm planing on calling her tomorrow or the day after and talking about it because actually hearing my voice instead of reading shit on a screen shows more emotion that wouldn't be translated through text.