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 = 2; b = 1; c = -6

= 2. - 6

= - 12

And either of their sum or difference = b

= 1

Thus the two terms are 4 and - 3

Difference = 4 - 3 = 1

Product = 4. - 3 = - 12

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

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

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

x = 3/2, x = -2

Roots of equation are 3/2, - 2