#### Answer

{$-10,-2,1,5$}

#### Work Step by Step

Since, $u^2+6u-27=0$
Factorize the expression as follows: $(u+9)(u-3)=0$
or, $u=${$-9,3$}
Replace $u$ with $(x-\dfrac{10}{x})$, we have
$(x-\dfrac{10}{x})=-9$
or, $x^2+9x-10=0$
or,$(x+10)(x-1)=0$
or, $x=${$-10,1$}
and $(x-\dfrac{10}{x})=3$
or, $x^2-3x-10=0$
or,$(x+2)(x-5)=0$
or, $x=${$-2,5$}
Hence, our solution set is $x=${$-10,-2,1,5$}