Answer
$x=5$ and $x=-\dfrac{3}{2}$
Work Step by Step
$\dfrac{10}{x}-\dfrac{12}{x-3}+4=0$
Multiply the whole equation by $x(x-3)$:
$10(x-3)-12x+4x(x-3)=0$
$10x-30-12x+4x^{2}-12x=0$
Simplify:
$4x^{2}-14x-30=0$
$2x^{2}-7x-15=0$
Solve by factoring:
$(x-5)(2x+3)=0$
So, we get two solutions, which are:
$x=5$ and $x=-\dfrac{3}{2}$
