A farmer has a rectangular field with dimensions $2m+7$ and $m-2$. If the field has an area of 51 square units, what is the value of $m$?

Area is given by the formula

Area = length*width

Filling in the given information, we have

51 = (2m+7) * (m-2)

2m² + 3m - 65 = 0

(m - 5) (2m + 13) - 0

m = - 13/2 or 5

Since dimensions of physical objects are non-negative, the value of m is 5.