The polynomial 2x³ − 9x² + ax + b, where a and b are constants, is denoted by f(x). It is given that (x + 2) is a factor of f(x), and that when f(x) is divided by (x + 1) the remainder is 30.
a. Find the value of a and the value of b.
b. When a and b have these values, solve the equation f(x) = 0.