Given $f(x) = (x - 4)(x + 3) + 4$. When $f(x)$ is divided by $(x - k)$, the remainder is k, find the value of k.

Given $f(x) = (x - 4)(x + 3) + 4$. When $f(x)$ is divided by $(x - k)$, the remainder is k, find the value of k.