Math - the polynomial x3-3x2-9x+c can be written in the form (x-a)2(x-b) if value of c is?

Writing a^b for a to the power b.
Expanding (x-a)^2(x-b) =(x^2-2ax+a^2)(x-b)=x^3+(-2a-b)x^2+(a^2+ 2ab)x-a^2b and comparing to the polynomial x^3-3x^2-9x+c we see that:
-2a-b=-3 (1)
a^2+2ab=-9 (2)
-a^2b=c (3)
solving for b in (1) we have b=3-2a and substituting into (2) we get
a^2+2a(3-2a)=-9
a^2+6a-4a^2=-9
-3a^2+6a+9=0
a^2-2a-3=0
(a-3)(a+1)=0
We conclude that:
(a=3, b=3-2(3)=-3 and c=-(3)^2(-3)=27) or (a=-1, b=3-2(-1)=5 and c=-(-1)^2(5)=-5)
Our answer is that c=27 or c=-5.