You can write the inequality, by factoring out 3x^{2}, as follows
3x^{2}(2x-3)<0 by inspection the roots are x=0 and x=3/2. so for x<0 the inequality is satisfied because 2x-3 <0 when x<0 and the inequality is satisfied when 0<x<3/2. When x>3/2 the function is positive so the inequality is not satisfied.
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