Answer
$x=-\dfrac{7}{2}$
Work Step by Step
$4^{3x-7}=32^{2x}$
Rewrite $4$ as $2^{2}$ and $32$ as $2^{5}$:
$(2^{2})^{3x-7}=(2^{5})^{2x}$
Multiply the exponents on both sides of the equation:
$2^{6x-14}=2^{10x}$
If $2^{6x-14}=2^{10x}$, then $6x-14=10x$
$6x-14=10x$
Solve for $x$:
$6x-10x=14$
$-4x=14$
$x=\dfrac{14}{-4}$
$x=-\dfrac{7}{2}$
