Switching memory from a gateway to a dell

Hello,
some one gave me a Gateway laptop p-6312 with windows vista and 1 gb memory. I really hate this computer. I swear it's cursed, However I have a dell laptop 9300 which I love. but it only has 512 mb memory and it's running windows XP. I would like to speed it up. can I take the Memory from the gateway laptop and put it in the dell ?
This is what was in the Gateway
2Rx16 PC2-5300S-555-12-A3

Dell
1Rx16 PC2-4200S-444-10-C1

I already checked and the Dell can be upgraded to 1gb

am I going to mess them both up if I do this...