Algae is a plant and the nitrates - the final stage of your nitrogen cycle - are a fertilizer. They feed and encourage the algae to grow. Brown algae will grow where there is insufficiant light to grow the green, plush algae that the fish so love to eat.
The best way to rid the tank of brown algae is to up the light - creating the bright green, nutricious algae that your goldies can snack on - and adding a soft carpet to the tank.
Ify ou do not like algae, though, keeping your nitrates as low as possible - 20 and under at all times - will discourage the algae. Very little food to feed it means very little algae. Elbow grease will remove the rest. I wipe the glass of the tank every water change and any place else I do not want algae growth. I scrub my fake plants every few weeks to clean them up. You can also soak them in bleach 1:10 and this will clean them beautifully. (10 minutes - no longer and follow with a dechlor bath)
I do not recommend the use of Algae Destroyer in a tank. It is an herbacide. It is a poison. The trick with this type of poison is to add enough that it kills the things you want it to kill without having it kill the things you do NOT want it to kill - ie: the fish. That is too fine a line for me to walk. It is far safer and more environmentally responsible to simply use a bit of elbow grease and keep the nitrates low.
A word of caution - if you DO use Algae Destroyer, NEVER use the fish water to water plants, pour on the garden or lawn or allow a cat or dog to lick up the water in any fashion.