210. Find the integer values of $x$ for which $x^{2}+5 x-12$ is divisible by 6.
210. The problem reduces to finding integer values of $x$ for which $x^{2}+5 x$ is divisible by 6. First, we find those values of $x$ for which $x^{2}+5 x$ is divisible by 3. For this, we note that for $x=0$ and $x=1$, the number $x^{2}+5 x$ is divisible by 3; therefore, $x=3 t$ and $x=3 t+1$. From these values of $x$, we need to select those for which $x^{2}+5 x$ is divisible by 2; but $x^{2}+5 x$ is an even number for any integer $x$; therefore, $x^{2}+5 x-12$ is divisible by 6 for $x=3 t$ and $x=3 t+1$, where $t$ is any integer.