In splitting method how did we obtain (x-3) ??

Solution 
From 2nd step,
f(x) = 5x² - 15x - 2x + 6 
       = 5x² ​​​​- (5 × 3)x - 2x + (2 × 3)
       = 5x(x - 3) - 2(x - 3) 
{Taking 5x common from first bracket and - 2 common from second bracket}
f(x) = (5x - 2)(x - 3)