I don't understand this math problem?

Question

The product of two consecutive even integers is 66 less than 9 times their sum. Find the two integers. Answer in the form of paired points with the lowest of the two integers first.

 

(_______ , ________) or ( _______ , _______)

Answer 1

If the first integer is x, then the next consecutive even integer is x+2

The product of two consecutive even integers would be:  (x) * (x+2)

66 less than 9 times their sum would be:  9* [(x) + (x+2)] - 66

 

Equate the two expressions and solve:

x * (x+2) = 9 * (x + x+2) - 66

(x^2) + 2x = 9 * (2x + 2) - 66

(x^2) + 2x = 18x + 18 - 66

(x^2) + 2x = 18x - 48

(x^2) + 2x - 18x + 48 = 0

(x^2) - 16x + 48 = 0

 

Factor the above equation so that:  (x-4) (x-12) = 0

So either (x-4)=0 or (x-12)=0

-->  x - 4 = 0  -->  x = 4

OR

-->  x - 12 = 0  -->  x = 12

 

If x = 4 : x + 2 = 4 + 2 = 6

If x = 12 :  x + 2 = 12 + 2 = 14

 

The paired points would either be (4,6) or (12,14)