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Mind-your-own-business, Soleirolia soleirolii, is a creeping perennial with tiny flowers and leaves. The branching stems root as they spread, forming a dense mat of foliage that few plants can grow through. The plant will soon take hold on any soil or lawn, although it's particularly prevalent in the crevices of stone walls and in damp conditions.
Solution
Organic
It will regrow from sections of stems left behind after hoeing or weeding, so you need to be thorough when trying to get rid of it, picking out any piece of foliage. If possible, get under the roots with a spade to slice it out. If it's in the lawn, carefully remove plants in April or September, then fork over the area and replace soil, re-sowing or turfing where necessary.
Chemical
In a lawn, bed or border, spot-treat patches of the plant using a total weedkiller, such as glyphosate. For best results, bruise the plant with the back of a rake or crush it underfoot before applying glyphosate. Avoid spraying on a windy day and near other desirable plants.
