Learn English – “solved in two different ways” or “solved by two different ways”

The answer, I'm afraid, is not very edifying.

We cheat.

We cast at least one verb into the active voice.

One way is to provide an indefinite subject such as "people" or "they" or "we":

What will happen when people start to use metallic elements, &c?

Another is to make the passive subject the active subject of the first verb:

What will happen when metallic elements start to be used, &c?

This is permitted with verbs like start,begin,continue,finish,stop which don't really signify an action but act as semi-auxiliaries to tell you the temporal "shape" of the action verb - what grammarians call its aspect.

Actions and tasks and projects can be "started" or "finished", but we speak of an object being "started" or "finished" only if it is being treated as a task or project: "I started my paper today" means "I started writing my paper".

Often, if you need to specify the agent for a passive construction, you're probably better off using the active voice. I would prefer "Can we solve this problem?" and "Have you shut the door?" to either passive. Use the passive (without an agent) where the emphasis is on the action, not the person(s) performing the action.