How about:
Sub ZeroKiller()
Dim N As Long, ToBeKilled As Range
Dim i As Long
N = Cells(Rows.Count, "A").End(xlUp).Row
For i = 1 To N
If Cells(i, "D").Value = 0 Or Cells(i, "D").Value = "" Then
If ToBeKilled Is Nothing Then
Set ToBeKilled = Cells(i, "D")
Else
Set ToBeKilled = Union(ToBeKilled, Cells(i, "D"))
End If
End If
Next i
If Not ToBeKilled Is Nothing Then
ToBeKilled.EntireRow.Delete
End If
End Sub
This assumes that A is the longest column. If this is not always the case, use:
N = Range("A1").CurrentRegion.Rows.Count
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