\[\frac{c^{2} + c - 6}{7c + 21} = \frac{(c - 2)(c + 3)}{7 \cdot (c + 3)} =\]
\[= \frac{c - 2}{7}\]
\[c^{2} + c - 6 = (c - 2)(c + 3)\]
\[c_{1} + c_{2} = - 1;\ \ c_{1} \cdot c_{2} = - 6\]
\[c_{1} = - 3;\ \ c_{2} = 2.\]