I need a equation for a problem in using a pulling force a mass a coefficient of static friction a coefficient of kinetic friction and solving for the frictional force

The minimum pulling force required to start it moving is

equal to the static frictional force.

F = (mass) x (gravity) x (coefficient of static friction).

Once it's moving, the force required to keep it moving at a steady speed,

without speeding up or slowing down, is the force of kinetic friction.

F = (mass) x (gravity) x (coefficient of kinetic friction).

In both equations, [ (mass) x (gravity) ] is just the object's 'weight'.