How do you factor -8w+49w^2+14w^3-28?

Collect $2 w$ between the first and third term and $7$ between the second and rourth:
$2 w \left(- 4 + 7 {w}^{2}\right) + 7 \left(7 {w}^{2} - 4\right) =$ collect $\left(7 {w}^{2} - 4\right)$
$= \left(7 {w}^{2} - 4\right) \left(2 w + 7\right)$