Aplot of land doubles in size by adding x meters to the length and x meters to width of land. if the original plot had an area of 200 by 300 meters, what is the value of x?

The original plot of land had dimensions (200 m)(300 m) = 60000 m^2, which is the product of L and W.

Twice that area would be 2(60000 m^2) = 120000 m^2 = (L+x)(W+x).  Expanding this, we get LW + Lx + Wx + x^2 = 120000 m^2.  Treat L and W as constants and x as the variable:

x^2 + (L+W)x + LW -120000 = 0 and LW=60000 (from above).

Substituting, 

x^2 + (L+W)x + 60000 - 120000 = 0, or x^2 + (L+W)x - 600000 = 0.  Unfortunately, we don't know the value of L+W  (unless we assume that L = 300 m and W = 200 m).  We could use the quadratic formula to solve the above equation for x in terms of (L+W).

I note that you wrote, "If the original plot had an area of 200 by 300 m^2 "

This is inappropriate and should read "If the original plot of land had DIMENSIONS 200 m by 300 m ...   

Ensure that you have copied down the original problem exactly as it was presented to you.