Answer
$x=\{ -5,-1 \}$
Work Step by Step
The factored form of the given equation, $
\dfrac{28}{x^2-9}+\dfrac{2x}{x-3}+\dfrac{6}{x+3}=0
,$ is
\begin{array}{l}\require{cancel}
\dfrac{28}{(x+3)(x-3)}+\dfrac{2x}{x-3}+\dfrac{6}{x+3}=0
.\end{array}
Multiplying both sides by the $LCD=
(x+3)(x-3)
,$ then the solution to the given equation is
\begin{array}{l}\require{cancel}
1(28)+(x+3)(2x)+(x-3)(6)=0
\\\\
28+2x^2+6x+6x-18=0
\\\\
2x^2+12x+10=0
\\\\
x^2+6x+5=0
\\\\
(x+5)(x+1)=0
\\\\
x=\{ -5,-1 \}
.\end{array}
