The different research trees require a wide span of speed ups. The research time varies from a few minutes to many days.
In order to waste as little speed ups as possible, you can prepare your speed ups to fit the expected timeframes in the research tree.
The Speedup Factory is usually used for investing time to build bigger speed ups, but at the top of the factory screen, there are something called Break up. The button is shown in the picture below.
This button gives you the possibility to first choose what type of speed up you need, then choose the speed up you will break up. See below for the steps.