Answer
$-43$
Work Step by Step
We know that for a matrix
\[
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
\]
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
Hence here $D=3(-4-12)-5(2-24)+7(-3-12)=3(-16)-5(-22)+7(-15)=-48+110-157-43$