could someone help with this equation, please?

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

 

Let n = an even number

Let n + 2 = the next consecutive even number

 

Their product = n(n + 2)

Their sum = n + n + 2 = 2n + 2

 

Since the product of the 2 is 66 less than 9 times their sum, we have

 

    n(n + 2) = 9(2n + 2) - 66

   

    n² + 2n = 18n + 18 - 66

   

    n + 2n - 18n = -48

   

    n - 16n + 48 = 0

 

    (n - 4)(n - 12) = 0

 

We use the zero product property to solve for n

 

     n - 4 = 0

     n = 4

 

       ***   numbers are 4 and 6

 

      n - 12 = 0

      n = 12

 

        ***  numbers are 12 and 14