If (3a + 6b + c + 2d) × (3a – 6b-c+2d) = (3a – 6b + c – 2d) × (3a + 6b – c – 2d), then Which one of the following is correct ?

=> (3a + 6b + c + 2d) (3a – 6b-c+2d) = (3a – 6b + c – 2d) (3a + 6b – c – 2d)

=>

$$\frac{(3a + 6b + c + 2d)}{(3a – 6b + c – 2d)}=\frac{(3a + 6b – c – 2d)}{(3a – 6b-c+2d)}$$

=>

$$\frac{((3a+c) +(6b+2d))}{((3a +c)-(6b+2d))}=\frac{((3a -c)+(6b-2d))}{((3a -c)-(6b-2d))}$$

using componendo and dividendo concept

=>

$$\frac{3a+c}{6b+2d}=\frac{3a -c}{6b-2d}$$

=>

$$\frac{3a+c}{3a-c}=\frac{6b+2d}{6b-2d}$$

=>

$$\frac{3a}{c}=\frac{6b}{2d}$$

=>

$$ad=bc$$

hence Answer is (C)