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How to do it:
The Very Simple Version:
-Put 3 inch clippings in a glass of water, leave until roots sprout and are about 1 inch long
-Carefully plant in dirt (same type of dirt as the plant you got the clippings from is in)
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First I took multiple 3 inch long (or so) clippings from a variety of Coleus plants and put them in glasses of water. I trimmed off the biggest leaves and just left two or four leaves at the ends of each stem. I left about an inch to an inch and a half of stem under the water. These stems had a tendency to curl after a few days in the water, so I had to periodically shift the plants so that they would stay submerged.
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After 4-5 days I started seeing roots growing off the stems. Depending on the plant, it may take a bit longer than this for the roots to start.
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It took a few weeks before the first new buds grew from the plants, but once they did the plants took off (as shown in this not so great photo). Can't wait to put them outside once it's warmer out! In terms of taking care of the Coleus, you can leave them in full or partial sun indoors, and water periodically (the leaves will droop when they really need water, but will spring back up when you water them!). More on coleus and what happens in different light conditions here.
Update: It's flowering!