Hot water along with laundry detergent will kill flea eggs on clothing and bedding so when you wash clothes or bedding that has fleas on them or flea eggs make sure to use the hot water setting on your washing machine and also laundry detergent.
You could also wash the clothes in some flea shampoo to help kill the fleas and flea eggs even better.
Then when you run the clothing through the dryer on the hot setting that hot dryer should also ensure the flea eggs and fleas are killed by the hot temperature of the dryer.
When your pet has fleas make sure to bathe them using flea shampoo and warm water and also use flea drops on their bodies.
Having the dog or cat professionally flea dipped as well is another good option to kill fleas and flea eggs on your pet.
To kill fleas and flea eggs on carpet you can buy some flea powder for carpet and then sprinkle it on the carpet and allow it to sit in the carpet overnight.
Then the next morning vacuum the carpet to remove the dead fleas and the flea powder.
Or you can also sprinkle some diatomaceous earth on the carpet and do the same thing.