Using the splitting middle term - the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 6; b = 11; c = 3

= 6.3 = 18

And either of their sum or difference = b

= 11

Thus the two terms are 9 and 2

Sum = 9 + 2 = 11

Product = 9.2 = 18

3x(2x + 3) + 1(2x + 3) = 0

(3x + 1)(2x + 3) = 0

(3x + 1) = 0 or (2x + 3) = 0

x = (-1)/3 or x = (-3)/2

Roots of equation are ,