#### Answer

$x = 6, -1$

#### Work Step by Step

$\frac{x-1}{x+2} = \frac{10}{3x-2}$
$(x-1)(3x-2) = 10(x+2)$
$x(3x-2) -1(3x-2) = 10x +20$
$3x^{2}- 2x -3x +2 = 10x +20$
$3x^{2} - 5x +2 = 10x +20$
$3x^{2} -5x + 2 -10x -20 = 0$
$3x^{2} -15x -18 = 0$
$3(x^{2} - 5x - 6) = 0$
$3(x-6)(x+1) = 0$
$x = 6, -1$