How do you divide 6x2-7x-5:3x-5

You can do long or synthetic division, I usually do the long division just as my preference ...

(6x^2-7x-5) / (3x-5)

2x remainder 3x-5

1 remainder 0

so the quotient is (2x+1)

which gives you the equivalent expression (2x+1) (3x-5) to what you started with ...