SOLUTION: Find all pairs of consecutive even integers such that ten less than their product is the sum of five times the smaller even integer and three times the larger even integer

Question 998561: Find all pairs of consecutive even integers such that ten less than their product is the sum of five times the smaller even integer and three times the larger even integer
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the smaller one x. The larger must be x + 2.
Now we can write
x(x+2)-10=5x+3(x+2)
Now we solve this...
x^2+2x-10=5x+3x+6 = 8x + 6
Combining like terms we get
x^2-6x-16=0
Factoring we get
(x-8)(x+2)=0
x = 8 and x = -2
Thus
x+2 = 10 and x+2 = 0
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