Been having some difficulty with the following question:

Prove that if the roots of:

x^3-ax^2+bx-c=0 are in arithmetic sequence then 2a^3-9ab+27c=0

Hence, solve for x in the equation x^3 -12x^2+39x -28=0

I've tried putting general forms of the roots as:

(x-a),(x-(a+d)),(x-(a+2d))

and then substituting them into the initial equation and setting = 0, but it hasn't gotten me anywhere.

Any help would be greatly appreciated