how do record purchased car

Use two different asset accounts to track the cars, and two different accounts for the new car:

1) Depreciate the old car down to 9,250, 'cause that's all it was worth when you traded it in.

2) Create a new asset account for the new car and enter 46,328.23 as the balance, using a new liability account (more or less a loan) as an offsetting account 'cause that's what it was worth and what you owed at the moment of purchase.

3) Transfer the old car's value of 9,250 to the liability account to reduce the balance

4) Similarly, in the credit card account, use the liability account for the 1k payment and 5k payments when you record those transactions.

5) Also, use the liability account for the 31,078.23 payment by check.

In the end, the liability account will have a 0.00 balance and the new asset account a 46,328.23 balance.

If course the new car isn't worth that you paid anymore, so perhaps use https://www.edmunds.com/ or similar site to value the new car and depreciate it as well.