I'm not really an expert in this, but here's how I do it.

L X W = 288

(L+1) (W-1) = 285

LW - 1L + 1W - 1= 285

LW - 1L + 1W = 286

then i do this:

.....LW - 1L + 1W = 286

(-) LW = 288

----------------------------

..... -L + W = -2

..... W = -2 + L

then i substitute to L x W = 288

L x W = 288

L (-2+L) = 288

-2L + L2 = 288

L2 -2L - 288 = 0

(L-18)(L+16) = 0

L = 18

L = -16 (this one is rejected because a rectangle cannot have negative sides)

then substitute to get the value of W

L x W = 288

18 x W = 288

18W = 288

W = 16

Answer would be{L=18,W=16}

That's how i do it. Sorry if I don't know how to put into math code.