There are few specific equations that need to be considered:

∑ F̅ = 0

Here in this equilibrium state, the rigid body will have no effects with external forces.

∑ F̅_x= 0

∑ F̅_y = 0

∑ F̅_z= 0

In these three equations there will be no moment as the result out of any direction x, y or z.