The number of positive integers $k$ for which the equation
\[kx-12=3k\]
has an integer solution for $x$ is
$\text{(A) } 3\quad \text{(B) } 4\quad \text{(C) } 5\quad \text{(D) } 6\quad \text{(E) } 7$
$\fbox{D}$
$kx -12 = 3k$
$-12=3k-kx$
$-12=k(3-x)$
$\frac{-12}{k}=3-x$
Positive factors of $-12$:
$1,2,3,4,6,12$
6 factors, each of which have an integer solution for $x$ in $\frac{-12}{k}=3-x$