Garden Width with Walkway Area

A rectangular plot of land is being developed into a garden. The length of the garden is twice its width. Surrounding the garden is a walkway of uniform width $x$ feet.

If the total area of the garden plus the walkway is 1,200 square feet, what is the width of the garden?

Let $w$ be the width of the garden. Thus, the length can be expressed as $2w$. The overall dimensions of the garden plus the walkway become $(2w + 2x)$ by $(w + 2x)$.

Your task is to find the width $w$ of the garden when equating the total area to 1,200 square feet.