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How long should you wait until you reapply for the same card, or any?
What's about American express, my mom has one and they keep denyin my application, if she signs me up as a co-borrower with them, would that put me on their good side?

Thanks

You should definitely wait.

First, the lender who denies your application should explain why you were not approved (usually referring to your credit report from a particular agency). If that's the case, you should only re-apply when you have good reasons to believe that your credit score at the agency has improved - for example, if you paid off some of your debt, if you got approved for another card, etc etc.

In general, you should wait at least 6 months before reapplying for the same product. It's highly unlikely you'll get approved any sooner - credit bureaus are relatively slow organizations and even if your factual information changes (e.g. you paid off your other cards), it will still take them a while to reflect that on your credit report.

Re: co-signing. The rules are different with each issuer. In this case, I'd recommend asking your mom to call American Express and ask if she could co-sign with you. Most likely it won't be a problem, the only question is whether the card will be reported as your card (helping you build your credit history) or your mom's card (not helping you in any way).