If the equation ends up false, like 4=5, there are no solutions. If it ends up true, there are an infinite amount of solutions. If it ends up as a concrete answer, like x = 1, there is one solution:
5(x-3) = 7x - 2(x+1)
5x - 15 = 7x -2x - 2
5x -13 = 5x
-13 = 0
So, there is no solution.
Hope this helped!