Answer
Solution set = $\{-1\}$.
Work Step by Step
First, we exclude those values of x that yield a zero in any of the denominators.
$x\not\in\{4 \}\qquad (*)$
The first denominator $3x-12$ is factored as $3(x-4)$
Multiply the equation with the LCD=$3(x-4)$
$ x+6=5(3)+2(x-4)\qquad$ ... simplify (distribute)
$x+6=15+2x-8$
$ x+6=2x+7\qquad$ ... add $-6-2x$
$-x=7-6$
$-x=1 $
$ x=-1\qquad$ ...Checking (*), this is a valid solution
Solution set = $\{-1\}$.
