Function Transformations: tranformation on a polynomial (also transformed)

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I have this polynomial in factored form that is already transformed:

f(x) = $a(x-b)^2(x-c)$, where a,b,c are real constants

This function is then transformed to a new function g(x), the following transformations were applied to function f(x):

1) reflected in the x-axis

2) Horizontally stretched by a factor of 1/2

3) Horizontally translated 3 units to the right.

After these transformations the new function g(x), the graph of g(x) goes thru the following points:

1) (-5,0)

2) (3,64)

3) (7,0)

FIND the values of a,b and c of the original function f(x)! End of Question

I tried to just plug in the points and then i would have a system of equations to solve. BUT it seems really difficult to solve these because the equation is non-linear. SO I am guessing that there must be another way. I can't think of what the other way could possibly be.

Here is my g(x) function:

g(x) = $-a(0.5(x-b)-3)^2(0.5(x-c)-3)$ // Hope i got this part right

Hope someone out there can help out here.