Mutazili theology organised itself around five principles, and the school treated holding all five, rather than any one of them, as what made a person a Mutazili.
The first is tawhid, the divine unity, taken in a strict sense. The attributes of God are not entities standing alongside the essence, because that would make eternal things other than God himself. God knows by his essence rather than by a knowledge distinct from it, and the Quran, being speech, is something God does rather than something God eternally is, and is therefore created.
The second is adl, justice, and it does the heaviest work in the system. God cannot do wrong, not because some external rule forbids it but because wrongdoing is incompatible with what God is. Good and evil are accordingly real properties that human reason can recognise without waiting for revelation, and God will not act against them. From this the school derived human free agency, because a person must genuinely originate their own acts or the reckoning at the judgement would punish someone for what God had done.
The third and fourth are the promise and the threat, meaning that God will certainly carry out both and cannot simply waive the second, and the intermediate position, which places a Muslim who commits a grave sin in a category between belief and unbelief rather than forcing the choice between them.
The fifth is commanding right and forbidding wrong, understood as a duty on the community which could in principle extend to acting against an unjust ruler.