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Factor the trinomial by grouping 6m^2-5m-4

Need to factor this trinomial, and not having much luck.

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Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
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Try to break the second term into two. Let us try to present 5m as 2m+3m.
6m2-3m-2m-4. Now let us group terms together.
(6m2-3m)-(2m+4) Factor out common factors.
3m(2m-1)-2(m+2). There is no way to factor further. Let us try different grouping.
(6m2-2m)-(3m+4)=2m(3m-1)-(3m+4) Again, no luck. 
Let us try this:
6m2-5m-4=6m2-8m+3m-4=(6m2-8m)+(3m-4)=2m(3m-4)+(3m-4). Now we got a common factor at last!
Factor (3m-4) out to obtain: