Arithmetic Sequences - Definition & Examples

$a,12,c,d$ is an arithmetic sequence with common difference $x$ such that $a,c,d$ is a geometric sequence. Given that $x$ is not $0$, what is the value of $x?$

Source: Lexington Math Tournament

(Note: You may or may not know what a geometric sequence is. The important thing to note here is that there exists a real number $y$ such that $ay = c$ and $cy = d$.)