Please help factor my homework question. thanks! 

(2q+5)(3q-4)= 0

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That's already factored!

Now you use the zero-factor theorem to 
set each factor = 0

   2q+5 = 0
     -5  -5
  ----------
   2q   = -5
      q = -5/2 

   3q-4 = 0
      4   4
  ----------
   3q   = 4
      q = 4/3 

The solutions are -5/2 and 4/3

Edwin