Let the length of the rectangle be x + 3
Let the width of the rectangle be x - 2
Recall, the area of a rectangle is length * width
Given that area of this rectangle is 150, it means that
(x + 3)(x - 2) = 150
Multiplying each term inside the bracket by the term outside, it becomes
x^2 - 2x + 3x - 6 = 150
x^2 + x - 6 - 150 = 0
x^2 + x - 156 = 0
We would find two terms such that their sum or difference is x and their product is - 156x^2. The terms are 13x and - 12x. Thus, we have
x^2 + 13x - 12x - 156 = =
x(x + 13) - 12(x + 13) = 0
x - 12 = 0 or x + 13 = 0
x = 12 or x = - 13
The value of x cannot be negative because it will make the length and width to be negative. hence,
x = 12
