Scale insects suck the sap of host plants. They can be serious pests on woody plants and shrubs, killing off branches and even whole plants and trees. They are not immediately identifiable as insects, since they lack a separate head and do not noticeably move. Ants protect scale insects from parasites and predators to farm the honeydew that scales produce. Therefore, curbing the ant population can wipe out scales. If they don't move, why are they hard to exterminate? Because of their protective waxy armour---which makes them easy to knock off with mild detergent.
Dilute Simple Green detergent, since it is packaged in concentrated form. Simple Green is designed to be custom-diluted to the task at hand by the user. The dilution ratio can be as high as 30-to-1 for scale application. Dip a toothbrush into the diluted solution and scrub away on all the scale insects. They should drop off the plant as their waxy coverings become slippery and lose adhesion to the plant. Continue scrubbing until they all fall off. Try a higher concentration if they don't yield.
Follow up occasionally with a horticultural soap or oil applied to the full plant. This can be sprayed on and still be effective---as this is one method used for large-scale crop treatment of scales. See the University of California-Davis webpage on scales cited below in Resources for the best time of the year for application.
Repeat application of Simple Green every six to 12 months.
Curb the ant population---which has a symbiotic relationship with scale insects---by attacking any nearby anthills with boiling water with liquid hand soap added in, or by soaking pipe tobacco in water overnight and pouring the liquid into the hill to effect nicotine poisoning. Another approach is to form a barrier at the base of the plant or tree with a collar of duct tape or a band of Tanglefoot. Diatomaceous earth, commonly used as a barrier for ants, may not be a good idea. It could also desiccate scale-eating insects you want to spare from the ants.
Note that Simple Green detergent is not to be confused with Simple Green Lime Scale Remover, which is designed to remove limescale mineral build-up from plumbing and dishwashers suffering from hard water.