help with gcse physics problem

A locomotive of mass 20000kg travelling at 28 ms^-1 heads towards a carriage of mass 8000kg heading in the other direction at 15 ms^-1. If the carriage rebounds from the collision at a speed of 10ms^-1 then what speed will be the velocity of the locomotive after the collision?

Again we need to find a total for the momentum before the collision.
Total momentum before = m₁v₁ + m₂v₂
Total momentum before = 20000 x 28 + 8000 x (-15)
Total momentum before = 560000 - 120000
Total momentum before = 440000kgms^-1
Therefore, the total momentum after the collision must be 440000kgms^-1.
m₁v₃ + m₂v₄ = 440000
20000v₃ + 8000 x 10 = 440000
20000v₃ + 80000 = 440000
20000v₃ = 440000 - 80000
20000v₃ = 360000
v₃ = 360000/20000 = 18ms^-1
I understand the first part but can someone explain what what the different numbers represent in the second part like m1v3 m2v4 20000v3 any help would be appreciated thanks

v1 and v2 are the velocities before the collision, and v3 and v4 are velocities after. Mass of the locomotives doesn't change. 20000v3 is the expression for mass x velocity of locomotive after collision.