The quick fix for BBA is dosing with a liquid carbon (Excel and Easycarbo are the two I know).
Any hardscape/hardware that can be removed from the tank I take out and scrub. Plants that are not rooted in the substrate (Anubias, Java fern) I also remove and spray the affected leaves with a solution of Excel (1 part Excel to 3 parts water), leave for about 10 minutes then rinse and return.
For plants that cannot easily be removed, I take off the worst affected leaves and spot dose what's left with Excel. I put the required daily dose for the whole tank into a syringe, turn off the filters and powerhead, shoo the fish out of the way and squirt the Excel directly onto the BBA. If there's a lot it can take a few days to get round it all, but it will see it off.
Then you have to work out why it attacked in the first place, because if you don't, it will more than likely be back.
Black Brush is a CO2 related algae and is brought on by low or fluctuating levels in the tank.
In high tech tanks the remedy is generally to increase the amount of CO2 and/or improve circulation around the tank.
In low tech tanks the water change regime may need adapting - tap water can have large amounts of CO2 dissolved in it, and that sudden influx can cause problems.
What lighting do you have in your tank? The strength of that basically decides whether the tank can be run without carbon supplementation.
Hope that helps.