How do you solve #2x^2+3x>0#?
The trick is to note that the sign of a polynomial expression can only be different at two points if the expression evaluates to
Solving for where it is
# <=> x=0 or 2x+3=0#
# <=> x=0 or x= -3/2#
Thus the intervals in question are
From here, we can just test a point in each to see what the sign of the expression will be:
Putting it together, then,