All goldfish grow very large, are very messy, and love to munch on plants. I have 5 goldfish in my outdoor pond that are 8" long, and oranda and other "short body" round goldfish can get to be the size of a softball or a grapefruit. They produce a significant ammount of waste, and just "having a strong filter" won't do anything for the build up of nitrates in the water. There is no way you could stuff enough plants into a 10 gallon tank to soak up all the nitrates that 4 goldfish would produce unless they were very small ones (3" or less, and VERY heavily planted, but goldfish eat plants so it wouldn't stay heavily planted for long anyway). Besides the biological issues, there is not anywhere near enough space for 4 goldfish to live happily in a 10 gallon tank. That would be like you living in 10x12 bedroom with 3 other people and not being able to leave for any reason. Oh, and there's no toilet in your bedroom, so you would be pooping in the corner.