The sum is 12x3+18x2-10x+8
Again, nice problem. These are not super easy. You need to imagine the triangles in the figure and relate sides.
For instance: ADC, its hypotenuse is 15
For ABC, it is 20,
so 20/15 is the ratio between both triangles. Now let's choose the side with 'x'
x is one side of ADC, the corresponding side in ABC is 15 (the second longest sides). You need to rotate the triangles, etc ... That's the tricky part :)
So:
20/15 =15/x ----> x = 15*15/20 = 225/20 = 45/4
Which is C
Not sure whether it's too late to help you though!!!!
Also notice that it's kind of a product rule:
x * 20 = 15 * 15
I am sure the book explains a short way of getting to this equation, like sides opposite, blah blah, but what i told you is the reason. You asked for understanding it! Best luck!
Answer:
Width = 
Step-by-step explanation:
All we have to do is to use the method of changing the subject. First we know that length * width is equal to area.
Area = length * width
We have the area and the length but we don't have the width. So we substitute the values we have int the equation and make the width (w) the subject.
(c^2 - 4x - 12) = (x + 2) * w
(c^2 - 4x - 12) = w(x +2)
Divide both sides by (x+2) so w can stand alone.

w = 
Angle Q and angle S equal 61
Answer: Both the equations when solved have different answers, the solutions for both the equation are given below. In the the first equation 4 (x-3)=16 , 4 is multiplied with both the terms in the bracket. Whereas, in the second equation 4x- 2 = 16 there is no variable to multiply with the LHS equation
Solution:
4 (x-3)=16
4x - 12 = 16
4x = 16 + 12
4x = 28
x = 7
4x - 3 = 16
4x = 16 + 3
4x = 19
x = 19/4
x = 4.75