Question

V = x(16-2x)(19-2x) = 175 ft³

Ok, thanks. Now I'm trying to multiply out and having some difficulty. I am getting 4x^3-70x^2+304x = 175 which I'm not sure how to work with

Answer 1

I agree it is a little difficult to solve unless you have learned Newton's method. If not, you can solve it by the bisection method, which is to evaluate the function using trial values of x until the function evaluates to 175.
I will give you a kick-start.
Let
f(x)= x(16-2x)(19-2x)
and knowing that the solution is around 0.68, we try
f(0.6)=0.6(16-2*0.6)(19-2*0.6)=158.064
f(0.7)=179.872
f(0.65)=169.124
So the next tries should lie between 0.65 and 0.7.
Keep on trying until you get a solution to within 1 or two decimals.

Answer 2

Here is a graph of the function f(x).
http://i263.photobucket.com/albums/ii157/mathmate/Ash.png