<s>[INST] Find the length and width of rectangle when you are given the area The area of a rectangle is $x^2 + 4x - 12$. What is the length and width of the rectangle? 
The solution says the main idea is to factor $x^2 + 4x -12$.
So, since $-12 = -2 \times 6$ and $-2 + 6 = 4$, it can be written as $x^2 + 4x - 12 = (x - 2)(x + 6)$
since the length is usually the longer value, the length is $6$ and the width is $-2$. 
I don't understand the logic to this solution at all. I understand $\text{length} \times \text{width} = \text{area}$, but outside of this information I don't understand how they got to this solution from the given information in the problem.  
 [/INST] The length is $(x+6)$ and the width is $(x-2)$.
The area is $(x+6)(x-2)=x^2+4x-12$
You may take this answer as the length is 6 units longer and the width is 2 units shorter than a give number $x$
For example, given $x=10$, you may get that the area is $10^2+4\times10-12=128$, or, the area is $(10+6)(10-2)=16\times8=128$
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