Factor completely by grouping 3u^2+8u-3

3u^2+8u-3

with grouping, we have to find 2 numbers which add up to 8 and multiply to 3 * (-3) = - 9.

testing, we find that 9 and - 1 add up to 8 and multiply to - 9.

so now we can write the original equation as

3u^2-u+9u-3

you can factor the terms in pairs:

u (3u-1) + 3 (3u-1) =

(u+3) (3u-1)