Help with maths question pls

discombobulated
ok this is the question:

f(x) = 6x2 + 12x + c where C is a constant.
a) Given f(x) =0 has equal roots, find the value of C.

so this what i did for this part:

b2- 4ac = 0 (formula for discriminant)
122-4(6xC) =0
144-24c=0
6-C=0
c=6 (is that right?)

Now for the next part:
b) Hence, solve f(x) = 0

6x2+12x+6=0
(x=1)(6x+6)=0
x=-1 x= -6/6 = -1

I wasn't really sure what i was doing but i tried to work it out and this is what i did but I'm not sure if it's right. (i don't think it is!) Can somebody help please!