posted by greg .
Consider the function f(x)=12x^5+30x^4–160x^3+5 .
f(x) has inflection points at (reading from left to right) x=D , E , and F
Look for points where f''(x) = 0. This will require solving a cubic equation. One factor will be x, so that you can factor a quadratic oput of that, and solve it easily.