So, first thing you do is set up an equation.
(3x-2)(x+6)=103 + (x-1)(2x) because the formula for area is length x width. First parentheses represent length and second represents width. Then, if the shaded region is listed as 103, the unshaded part’s area can be written as length x width.
Solve for x by using the FOIL method or the table method, as you did in your work.
3x^2 - 20x - 12 = 3x^2 - 2x + 103
Here’s a helpful tip- whenever you get the same term on both sides of an equal sign, you can just erase them because they cancel each other out. This is because if you go on the opposite side of an equal sign, you do the inverse operation (example- +40 turns into -40 on the other side).
Simplify and it becomes -22x-115.
-22 is a factor of -115. Divide them and you get 5.
-22(x-5).
Since this is a quadratic equation, to find x, you set it equal to 0.
-22(x-5) = 0.
We know that at least one of the two factors must be 0, because anything multiplied by 0 equals 0. If -22 is not equal to 0, it must be x-5.
x-5=0.
Simplify and use the inverse operation.
x=5.
Then, substitute it back into the dimensions of the inside rectangle and you get
4, 10