Just to add to the good advice you've already received.

Check your nitrates and phosphates and work on those. Algae loves both.

I suspect that the sludge in the bottom of the tank is the real culprit -
vacuum out as much out as possible - strip down as much as possble to
acheive this.

Check your tap water for nitrates and phosphates, the source water could
also be contributing. Doing water changes with tap-water that is high in
nitrates etc will not dilute the existing nitrates as much (or at least will
not get them down to the minimum required). Plan on doing lots of water
changes - perhaps 30 to 50% at a time a couple of times a week for a while
until the nitrates are under control. Having done this, you could add a
nitrate pad to your filter to keep it down.

Also, clean your filters regularly (maybe once or twice a week at first) in
tank water. The build up of detritus in the filter will often start feeding
nitrates back into the system.

Don't bother taking the chemical route, you need to fix the problem at
source which is too many algae feeding nutrients - nitrate and phosphate.

One other thought, in addition to the above, if you have planted aquarium,
you could also add some CO2 (if you don't have it already) to get your plant
growth up to it's maximum. Plants growing flat-out will use a lot more of
the excess nutrients and so depriving the algae.

Hope it helps

Mark