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.  

Forget about the $y$ for a second. 
If you want to factor $25x^2 + 5x - 6$, look for two numbers whose product is $25 \cdot -6 = -150$ and whose sum is $5$. It takes just a moment to see that the two numbers are $15$ and $-10$. Then:
\begin{align*}
25 x^2 + 5x - 6 &= 25 x^2 + (15x - 10x) - 6 \\ &= (25 x^2 + 15x) - (10x + 6) \\ &= 5x(5x + 3) - 2(5x + 3) \\& = (5x-2)(5x+3).\end{align*}
With the $y$ included the process is nearly identical:
\begin{align*}
25 x^2 + 5xy - 6 y^2&= 25 x^2 + (15xy - 10xy) - 6y^2 \\ &= (25 x^2 + 15xy) - (10xy + 6y^2) \\ &= 5x(5x + 3y) - 2y(5x + 3y) \\& = (5x-2y)(5x+3y).\end{align*}
