The floor of a shed has an area of 96 square feet. the floor is in the shape of a rectangle whose length is 4 feet less than twice the width. find the length and the width of the floor of the shed.

Alright in this one, you are going to need to factor. 
The width is x
The length is 2x-4
To find the area of a rectangle is L*W
so (2x-4)(x) when distributed is 2x^2 -4x

Then put that in the equation and you have:
2x^2 -4x = 96
2x^2 -4x -96 = 0  

2x^2+12x-16x-96=0
3x(x+4)-4(x+4)=0
(3x-4)=0
(x+4)=0
x=-4
x=3/4
Since length isn't negative
we will use 3/4 as x.

Width= 0.75 ft
Length= 1.5