The problem is how many people must attend the third show so that the average attendance for three shows is 3000? and the other show attendance numbers are 2580, and 2920

An average is just the total attendance numbers / the number of performances.

Let's let the number of people in the third show be equal to x so we can write this as a formula, it's easier to read. x is just "some number we don't know"

The average is

Average=Total attendance/3
So
3000=(2580+2920+x)/3

So let's multiply by that 3 on both sides, make x easier to find

Average*3=2580+2920+x ( * means multiplied)

The average is 3000

So

2580+2920+x=3000*3
2580+2920+x=9000
 

Then we subtract those other attendances to get x on its own.

x=9000-2580-2920
x=3500