A machine for closing and sealing cardboard boxes or other packaging cases with random sizes of cases presented. An input gate controls passage of cases onto at least one conveyor that moves the cases through the machine. An input positioning stage centers and squares the case. A measuring station performs a primary measurement of the width and height of the open case. A closing station and tape sealing station are adjusted to the primary case size measurement. The case closing station then closes the case. The side major flaps are closed using a major flap closer with crossed arms pivoted at separated pivot axes. The sealing station has a secondary or closed case measurement detector which more accurately adjusts the tape applicator height. Lateral support heads engage the sides of the case to prevent distortion while tape is applied.