Sam's plasma tv has a 14inby18in screen and border. The total area of the tv 480inch^2. How wide is the trim

You must be assuming the trim is uniform all around

let the width of the trim be x
(14+2x)(18+2x) = 480
252 + 64x + 4x^2 - 480 = 0
x^2 + 16x - 57 = 0

x^2 + 16x + 64 = 57+64 , (I completed the square)
(x+8)^2 = 121
x + 8 = ± √121
x = 3 or a negative value, which is no good

The trim is 3 inches wide

check:
TV has dimenstions 20 by 24 inches
area = 20 x24 = 480

all is good