Extracting the obvious common factor color(green)(""(3y)) should be fairly obvious.
The more difficult problem is whether the remaining factor color(brown)(""(2y^2+y-1)) has any factors.
Treating color(brown)(""(2y^2+y-1)) as a quadratic of the equation ay^2+by+c=0
and applying the quadratic formula: y=(-b+-sqrt(b^2-4ac))/(2a)
we would get
color(white)("XXX")y=(-1+-sqrt(1^2-4(2)(-1)))/(2(2))
color(white)("XXXX") = (-1+-3)/4
color(white)("XXXX")= -1 or +1/2
This implies color(brown)(""(2y^2+y-1)) has (incomplete) factors color(green)((y+1)(y-1/2))
Multiplying (y+1)(y-1/2) gives color(blue)(y^2+1/2y-1/2)
which implies that an additional factor of color(green)(2) is required.
So color(brown)(2y^2+y-1) = color(green)(2(y+1)(y-1/2)
orcolor(white)("XXXXXXX")=color(green)((y+1)(2y-1))