What value of c makes 3x^2+24x+c contain a perfect square trinomial

One way to determine the value of c is to do completing the square. We do as follows:

3x^2+24x+c = 0

3x^2+24x = - c

3 (x^2 + 8x) = - c

3 (x^2 + 8x + 16) = - c + 48

Since - c + 48 should be equal to zero thus,

-c + 48 = 0

c = 48