Answer
$a= -5, -1$
Work Step by Step
$\frac {28}{9-a^2} =\frac{2a}{a-3} + \frac{6}{a+3}$
$\frac {28}{(3+a)(3-a)} =\frac{2a}{a-3} + \frac{6}{a+3}$
$\frac {28}{(3+a)(-3+a)(-1)} =\frac{2a}{a-3} + \frac{6}{a+3}$
$\frac {-28}{(3+a)(-3+a)} =\frac{2a}{a-3} + \frac{6}{a+3}$
$\frac {-28}{(a+3)(a-3)} =\frac{2a}{a-3} + \frac{6}{a+3}$
$\frac {-28}{(a+3)(a-3)}*(a+3)=\frac{2a}{a-3}*(a+3) + \frac{6}{a+3}*(a+3)$
$\frac {-28}{(a-3)}=\frac{2a(a+3)}{a-3} + 6$
$\frac {-28}{(a-3)}*(a-3)=\frac{2a(a+3)}{a-3}*(a-3) + 6*(a-3)$
$-28=2a(a+3)+6*(a-3)$
$-28=2a^2+6a+6a-18$
$-28=2a^2+12a-18$
$-28+28=2a^2+12a-18+28$
$0=2a^2+12a+10$
$0=2(a^2+6a+5)$
$0=2(a+5)(a+1)$
$0\ne2$
$0=a+5$
$0-5=a+5-5$
$-5=a$
$0=a+1$
$0-1=a+1-1$
$-1=a$
$a=-5$
$\frac {28}{9-a^2} =\frac{2a}{a-3} + \frac{6}{a+3}$
$\frac {28}{9-(-5)^2} =\frac{2*(-5)}{(-5)-3} + \frac{6}{(-5)+3}$
$\frac {28}{9-25} =\frac{-10}{-8} + \frac{6}{-2}$
$\frac {28}{-16} =\frac{5}{4} + (-3)$
$\frac {7}{-4} = 5/4 -3$
$-7/4 = 5/4 -3$
$-7/4 =5/4 -12/4$
$-7/4 = -7/4$ (true)
$a=-1$
$\frac {28}{9-a^2} =\frac{2a}{a-3} + \frac{6}{a+3}$
$\frac {28}{9-(-1)^2} =\frac{2*(-1)}{(-1)-3} + \frac{6}{(-1)+3}$
$\frac {28}{9-1} =\frac{-2}{-4} + \frac{6}{2}$
$\frac {28}{8} = 1/2 + 3$
$14/4 = 7/2$
$7/2 = 7/2$ (true)