Determine a,b and c so that curve y= ax^3 + bx^2 + cx will have a slope of 4 at its point of inflection (-1,-5)

Help please!

-5 = -a+b-c

dy/dx = 3 a x^2 + 2 b x + c

= 4 at x = -1
so
3a - 2b + c = 4

d^2y/dx^2 = 0 = 6ax +2b = -6a+2b
so b = 3 a

3 a -6a + c = 4
-5 = -a +3a -c

-3a + c = +4
+2a - c = -5
------------
5 a = 9

etc check my arithmetic