At x=1, f'(x)=0.
x=1, y=3. The tangent at x=1 is parallel to the x-axis
(it's a local minimum).
If this tangent is tangent at another point, then there is a 2nd turning point at y=3.
Hence, we find a second solution for x, if y=3 corresponds to f'(x)=0 for more than one x.
This also means we can examine f(x) to see how many x causes f(x)=3.
f(x)=3 for x=1 and x=-2 only.
To check the tangent, if x=-2, f'(x)=-32+16+16+8-4-4=0.
Hence, The tangent is also tangent to the curve at (-2,3).