Factor $6x^2​ −7x−5=0$ I'm trying to factor
$$6x^2​ −7x−5=0$$
but I have no clue about how to do it. I would be able to factor this:
$$x^2-14x+40=0$$
$$a+b=-14$$
$$ab=40$$ 
But $6x^2​ −7x−5=0$ looks like it's not following the rules because of the coefficient of $x$. Any hints?

When in doubt, you always have the quadratic equation. But if you really want to do it this way, you have to consider how the dominant term can factor. Here, you have either $6=6\times 1$ or $6=3\times 2$, so $(6x+a)(x+b)$ or $(3x+a)(2x+b)$. Try both. In both cases, you get the Viete-like formulas, just like you wrote down, but with a few prefactors ($a+6b=-7$ and $ab=-5$ in the first case).
