Answer
$$\left\{ { - 2} \right\}$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
4 & 3 & 0 \cr
2 & 0 & 1 \cr
{ - 3} & x & { - 1} \cr
} } \right| = 5 \cr
& {\rm{Expand \,the\, determinant \,to\, obtain}} \cr
& - 2\left| {\matrix{
3 & 0 \cr
x & { - 1} \cr
} } \right| + 0 - 1\left| {\matrix{
4 & 3 \cr
{ - 3} & x \cr
} } \right| = 5 \cr
& - 2\left( { - 3 + 0} \right) - \left( {4x + 9} \right) = 5 \cr
& {\rm{Solve\, the\, equation}} \cr
& 6 - 4x - 9 = 5 \cr
& - 4x = 8 \cr
& x = - 2 \cr
& {\rm{The\, solution\, set\, is}} \cr
& \left\{ { - 2} \right\} \cr} $$
