taking LCM

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 = 10 ;b = - 3; c = - 1

= 10. - 1 = - 10

And either of their sum or difference = b

= - 3

Thus the two terms are - 5 and 2

Difference = - 5 + 2 = - 3

Product = - 5.2 = - 10

5x(2x-1) + 1(2x-1) = 0

(5x + 1)(2x-1) = 0

(5x + 1) = 0 or (2x-1) = 0