Answer
$6y^2+5y-6 = (3y-2)~(2y+3)$
Work Step by Step
Let's consider a trinomial in this form: $~ax^2+bx+c$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = a\times c$
Then the next step is to write the trinomial as follows:
$~x^2+bx+c = ax^2+rx+sx+c$
Let's consider this trinomial: $~6y^2+5y-6$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = 5$ and $r\times s = -36$. We can see that $(9)+(-4) = 5~$ and $(9)\times (-4) = -36$
We can factor the trinomial as follows:
$6y^2+5y-6 = 6y^2+9y - 4y-6$
$6y^2+5y-6 = (6y^2+9y) +(- 4y-6)$
$6y^2+5y-6 = (3y)(2y+3) +(-2)(2y+3)$
$6y^2+5y-6 = (3y-2)~(2y+3)$
