Find three consecutive even integers such that the product of the first and the third is equal to three times the second?

Answer 1

Let the 3 numbers be:

x, x+2, x+4

The product of the first and third would be x(x+4)=x^2+4x and set that equal to three times the second: 3(x+2)

x^2+4x=3x+6

set the equation equal to 0 by subtracting 3x and 6 from both sides.

x^2+x-6=0

Factor (x+3)(x-2)=0

solve: x=-3, x=2

since they want even integers, -3 is not the answer, so the answer for x is 2 and the three consecutive even integers are 2, 4, 6