The required values of x are x = {-2, 5}.

Given

$\rm x^{2} - 3x - 10 = 0$

$\rm or, x^{2} - (5 - 2) x - 10 = 0$

$\rm or, x^{2} - 5x + 2x - 10 = 0$

$\rm or, x( x - 5)  + 2 (x - 5) = 0$

$\rm or, (x + 2)(x - 5) = 0$

Either

$\rm (x + 2) = 0$

$\rm \therefore x = -2$

Or

$\rm (x - 5) = 0$

$\rm \therefore x = 5$