Actually, you want to hit the area with a high rate of RoundUp starting when the zoysia begins active green growth. Then you sod cut the brown sod out. Till the area. Watch for green shoots of zoysia and kill it again. It may take 2-3 years to kill zoysia in a cool season grass area. In mulch beds and planter areas, Sethoxydim will suppress zoysia that comes up around flowers, trees, and shrubs.
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Benjamin Franklin 1775
Sell not virtue to purchase wealth, nor Liberty to purchase power.
Benjamin Franklin Poor Richard's Almanac1738