Answer
The solutions are $x=-\dfrac{1}{3}$ and $x=\dfrac{7}{2}$
Work Step by Step
$\dfrac{7}{x^{2}}+\dfrac{19}{x}=6$
Multiply the whole equation by $x^{2}$:
$x^{2}\Big(\dfrac{7}{x^{2}}+\dfrac{19}{x}=6\Big)$
$7+19x=6x^{2}$
Take all terms to the right side of the equation and rearrange:
$0=6x^{2}-19x-7$
$6x^{2}-19x-7=0$
Solve by factoring:
$(3x+1)(2x-7)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$3x+1=0$
$3x=-1$
$x=-\dfrac{1}{3}$
$2x-7=0$
$2x=7$
$x=\dfrac{7}{2}$
The solutions are $x=-\dfrac{1}{3}$ and $x=\dfrac{7}{2}$
