Do the grouping $4u^{2}-10uv-6uw+15vw=\left(4u^{2}-10uv\right)+\left(-6uw+15vw\right)$, and factor out $2u$ in the first and $-3w$ in the second group.
$$2u\left(2u-5v\right)-3w\left(2u-5v\right)$$
Factor out common term $2u-5v$ by using distributive property.
