Answer
$$\left\{ { - {2 \over 3}} \right\}$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
{2x} & 1 & { - 1} \cr
0 & 4 & x \cr
3 & 0 & 2 \cr
} } \right| = x \cr
& {\rm{Expand \,the\, determinant\, to\, obtain}} \cr
& - 0 + 4\left| {\matrix{
{2x} & { - 1} \cr
3 & 2 \cr
} } \right| - x\left| {\matrix{
{2x} & 1 \cr
3 & 0 \cr
} } \right| = x \cr
& 4\left( {4x + 3} \right) - x\left( {0 - 3} \right) = x \cr
& {\rm{Solve\, the\, equation}} \cr
& 16x + 12 + 3x = x \cr
& 19x + 12 = x \cr
& 18x = - 12 \cr
& x = - {2 \over 3} \cr
& {\rm{The \,solution\, set\, is}} \cr
& \left\{ { - {2 \over 3}} \right\} \cr} $$
