Answer
$$\left\{ { - {4 \over 3}} \right\}$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
5 & x \cr
{ - 3} & 2 \cr
} } \right| = 6 \cr
& {\rm{Expand \, the\, determinant\, to\, obtain}} \cr
& \left( 5 \right)\left( 2 \right) - \left( { - 3} \right)\left( x \right) = 6 \cr
& 10 + 3x = 6 \cr
& {\rm{Solve\, the\, equation}} \cr
& 3x = - 4 \cr
& x = - {4 \over 3} \cr
& {\rm{The \,solution\, set \,is}} \cr
& \left\{ { - {4 \over 3}} \right\} \cr} $$
