Answer: The small brown discs attached to stems and the undersides of leaves are scale insects. The adult females have a waxy outer shell that protects them and makes it difficult for insecticides to reach them. You can wipe the scales off with a damp cloth or push them off with a Q-tip. After you've removed them all, spray the entire plant with a light summer oil to suffocate any remaining immature scale insects. Follow the label directions closely when applying.
When you bring new plants into the house, it's always safest to isolate them from the rest of your collection until you're sure they're not harboring any insect or disease problems.
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