3.67: Binomial expansion and coefficient equation

Expand $(2-3x)^{4}$, evaluating all of the coefficients.

The sum of the first three terms in ascending powers of $x$ in the expansion of $(1+x)^{n}(2-3x)^{4}$ is $32 + 16x + bx^{2}$. Find the values of $n$ and of $b$.