How to solve the pde $f u-{xx} − 3u_{xt} − 4u_{tt} = 0$?

Question

On factorizing the pde we get:

$$(∂_x − 4∂_t)(∂_x + ∂_t)u = 0.$$

If we let $w=u_x+u_t$ then $$w_x-4w_t=0$$ and so $w(x,t)=f(t+4x)$ and so $$f(t+4x)= u_x+u_t.$$ What do I do after this step?