First of all, we can factor a factor of [tex] 5 [/tex] from all terms:
[tex] 5 (3u^4-4u^3-7u^2) [/tex]
Then, we can factor [tex] u^2 [/tex] from all terms:
[tex] 5u^2 (3u^2-4u-7) [/tex]
To factor the quadratic expression in parenthesis, we must find its roots, which are [tex] -1 [/tex] and [tex] \frac{7}{3} [/tex]. This implies
[tex] 3u^2-4u-7 = 3(u+1)(u-\frac{7}{3})[/tex]
So, the complete factorization is
[tex] 5u^2 \cdot 3(u+1)(u-\frac{7}{3}) = 15u^2(u+1)(u-\frac{7}{3}) [/tex]
