factor the following expression $25x^2 +5xy -6y^2$ How to factor
$$25x^2 +5xy -6y^2$$
I tried with $5x(5x+y)-6y^2$. I'm stuck here. 
I can't continue.  

let me expand on my comment of using quadratic formula to factor an expression like this. of course, you need to have the quadratic formula that
$x = \dfrac{-b + \pm \sqrt{b^2 - 4ac}}{2a}$ are the solutions of 
$ax^2 + bx + c = 0.$ 
we will look at first the equation $25x^2 +5xy - 6y^2 = 0$ later on we will see how we can use the solutions to factor the expression. matching $25x^2 +5xy - 6y^2 = 0$ with $ax^2 + bx + c = 0$ we can identify $a = 25, b = 5y, c = -6y^2.$ first the discriminant $b^2 - 4ac = (5y)^2 - 4*25*(-6y^2) = 625y^2 = (25y)^2$
using the formula $x = \dfrac{-5y \pm 25y}{50} = -\dfrac{3y}{5}, \dfrac{2y}{5}$ 
we can turn this into two equations into the factors 
$k(x+\frac{3y}{5})(x - \frac{2y}{5}) = 25x^2 +5xy - 6y^2 = 0 $ matching the coeffcient of $x^2$ fixes $k = 25.$
what do we have now is $$25(x+\frac{3y}{5})(x - \frac{2y}{5})= (5x + 3y)(5x - 2y)= 25x^2 +5xy - 6y^2 = 0 $$ 
from the last equalities drop leftmost and the rightmost expressions and you have factored $25x^2 +5xy - 6y^2.$
