14+5n=-4n+17

Let's look at this one again

14+5n=-4n+17         add 4n to both sides

14 + 9n  = 17           subtract 14 from both sides

9n = 3                      divide both sides by 9

n = 3/9 = 1/3

Checking this in the original problem, we have

14 + 5(1/3) = -4(1/3) + 17

14 + 5/3 = -4/3 + 17

14 + 1 + 2/3   = -1 - 1/3 + 17

15 + 2/3  = 16 -1/3

15 + 2/3  = 15 + 2/3

So, 1/3 is our answer......

14+5n=4n+17

n+14=17

n=3