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 = 1; b = 12; c = 35

= 1.35 = 35

And either of their sum or difference = b

= 12

Thus the two terms are 7 and 5

Sum = 7 + 5 = 12

Product = 7.5 = 35

x(x + 7) + 5(x + 7) = 0

(x + 5)(x + 7) = 0

(x + 5) = 0 or (x + 7) = 0

x = -5 or x = -7

Roots of equation are - 5, - 7