12c^2+24cd+9d^2

Question

how do i solve it

Answer 1

Given 12c^2+24cd+9d^2

12c^2+24cd+9d^2 = 0

12c^2+18cd+6cd+9d^2= 0

6c(2c+3d)+3d(2c+3d) = 0

(6c+3d)(2c+3d) = 0

(6c+3d) = 0                       and          (2c+3d) = 0

6c = -3d                            and          2c = -3d

Divide to each side by 6.    and       Divide to each side by 2.

6c/6 = -3d/6                      and         2c/2 = -3d/2

c = -d/2 and c = -3d/2

And smilarly d = -2c and d = -2c/3

Solutons are c = -d/2,-3d/2 and d = -2c, -2c/3