How do I solve: 4y^2 - 11y - 3 =0 by factoring?

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How do I solve: 4y^2 - 11y - 3 =0 by factoring?

Mathematics
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Well, do you know how to factor by decomposition?
by decomposition?
Yeah, we compose the middle term into smaller terms

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decompose*
yes I do
but if I do that: (2y-...)(2y-...)
So what two numbers sum up to -11, and are multiplied to get -12?
to get -12?
Yeah?
ohhh, 4 x -3
i get it now
Its 12, and minus one, it has to also add up to -11
yup! okay, thank you!
Your welcome :), ill be here for a bit if you need anymore help
You can factor by grouping... \[4y^2-11y-3=0\] \[4y^2-12y+y-3=0\] Remove a 3 from the first 2 terms. \[4y(y-3)+(y-3)=0\] Factor out a (y-3) \[(y-3)(4y+1)=0\] Easy to find the zeroes from here.
Remove a 4y from the first 2 terms***
Why do I have to remove a 4y from the first 2 terms? And why is it now (y-3)(4y + 1)?

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