Answer
$$\left\{ { - {1 \over 2}} \right\}$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
x & 0 & { - 1} \cr
2 & { - 3} & x \cr
x & 0 & 7 \cr
} } \right| = 12 \cr
& {\rm{Expand \,the\, determinant\, to \,obtain}} \cr
& - 0 + \left( { - 3} \right)\left| {\matrix{
x & { - 1} \cr
x & 7 \cr
} } \right| - 0 = 12 \cr
& - 3\left( {7x + x} \right) = 12 \cr
& {\rm{Solve\, the \,equation}} \cr
& - 24x = 12 \cr
& x = - {1 \over 2} \cr
& {\rm{The\, solution\, set \,is}} \cr
& \left\{ { - {1 \over 2}} \right\} \cr} $$
