Explain, how in the long-run

Explain, how in the long-run, equilibrium with free entry and exit, firms under perfect competition earn zero abnormal profits.

A perfectly competitive firm in the long-run can earn normal profits only. In case an industry is showing supernormal profits (TR>TC or AR>AC) in short-run, new firms will join the industry leading to increase in supply and will shift market supply curve to the right. Accordingly market price will be reduced and supernormal profits will be wiped out.
In case of negative abnormal profits (losses) in the short-run when (TR<TC or AR <AC) some of the existing firms will leave the industry. Accordingly, supply will fall and market supply curve will shift to the left forcing the price to move up till the situation of zero normal profit is reached.