ZOOM does an excellent job whitening yellow to orange colored teeth. Whether or not it can help the brown stains depends a lot on what type of stains they are.
Did the teeth develop that way? If so, the brown stain may be more internal and not respond well to whitening. If the teeth developed that way, cosmetic bonding or porcelain veneers may be the only way to remove and/or mask the brown stain.
Did the brown stain happen over the last several years? If so, it may be more superficial and may respond after a professional cleaning and ZOOM whitening. ZOOM whitening is more effective once a patient has had their teeth cleaned to remove the extrinsic stain and tartar.
Our teeth discolor over the years from diet soda, juices, coffee, smoking, red wine, or other sources, and no tooth whitening is a permanent treatment. Some dentists recommend tray whitening to "touch up" and re-whiten, while others may recommend another ZOOM procedure.