What do you think about using this on dogs?

It helps with their dand-woof.

Why not try Selsun Blue?

Yes. What’s good for the master is good for the K9. Baby shampoo would be a better choice.

Don’t do it. Generally, human shampoos are too harsh for dogs. If you’re not using a shampoo designed for them, Dawn dish-washing soap is your best bet.

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I wouldn’t use Head and Shoulders or Selsen Blue for that matter those sort of shampoos have even more chemicals than usual, I would follow the advice of @syz .