Solve for x:  3x^{2} + 17x + 10 = 0 
Here are the possibilities for a and c that make ac = 3...  a = 1, c = 3 a = 3, c = 1 a = 1, c = 3 a = 3, c = 1 
and here are the possibilities for b and d that make bd = 12:  b = 1, d = 10 b = 1, d = 10 b = 2, d = 5 b = 2, d = 5 b = 5, d = 2 b = 5, d = 2 b = 10, d = 1 b = 10, d = 1 
Now find the combination of these that makes ad + bc = 17 Try out a problem here to get a feel for doing this. 
a = 3, c = 1 b = 2, d = 5 
Factorization:  (3x + 2) (x + 5) = 0. 
Set each factor equal to 0:  3x + 2 = 0, x + 5 = 0. 
Solve each equation:  x = 2/3, x = 5. 


