Every time I wash my bright shirts in the laundry machine, they always come out with new stains...?

Every time I wash my bright shirts in the laundry machine, they always come out with new stains which I end up having to wash out again or remove with a lint-remover. The stains are somewhat sticky and some of it is white, like dry soap. How do I avoid this? I just looked inside the washing-machine and it doesn't look filthy, but still my brights come out with stains. Help?