Why gun move backward after bullet is released?

Newton's third law - 'Action and reaction are both equal and opposite.' Basically, when the powder charge inside the bullet ignites, it exerts the same force to backwards as it does to launch the bullet down the barrel. Since the cartridge is fixed inside the chamber, the result is that the gun 'kicks back'.

There are two ways to consider this phenomenon. First, it falls under the general category of Newton's Laws of Motion, that for every action there is an equal and opposite reaction. Secondly, if you examine what is happening in detail, you would see that when a bullet is fired from a gun, there is an explosion which produces a rapidly expanding cloud of gas, which is what pushes the bullet to leave the barrel at high velocity. That same cloud of gas, which pushes the bullet forward, expands in every direction, not just forward, therefore it is also pushing the gun backward. The pressure in the various sideways directions (up or down, right or left) is symmetrical; it presses equally in opposite directions resulting in no net force. But the pressure on the bullet to go forward and the gun to go backward is not balanced in that manner, because it is divided between the bullet and the gun. Hence there is a net force exerted on both the bullet and the gun. The force exerted on the bullet is necessarily equal to the force exerted on the gun. Momentum is conserved, so you can't push something forward without also pushing something backward. (This is not always obvious, because sometimes we are pushing on the Earth, which is so large that we do not see any resulting movement.)