Sum Equals Zero

Both the Forces and Momenta need to be 0 in total. This is called statics. If they are not 0, the body is accelerated (=in motion). The equilibrium conditions are: ∑F = 0
∑M = 0
Accelerated bodies are subject of the advanced mechanics discipline called Dynamics.

Free-Body Diagram

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For calculating the forces and momenta, we need to draw the free-body diagram. Replace the reactions with forces:

The equilibrium conditions form a system of equations with unknowns, which can be rearranged to determine the desired quantities: $\sum \mathrm{F}\to =0={\mathrm{A}}_{\mathrm{H}}$ $\sum \mathrm{F}\uparrow =0={\mathrm{A}}_{\mathrm{V}}+\mathrm{B}-\mathrm{F}$ $\sum {\mathrm{M}}_{\mathrm{B}}\circlearrowleft =0=\mathrm{F}·\frac{\mathrm{l}}{2}-{\mathrm{A}}_{\mathrm{V}}·\mathrm{l}+\mathrm{M}$