An example for three consecutive even integers is 2, 4, 6 or 10, 12, 14, or 28, 30, 32.
What do you notice about the difference between each consecutive number? (Yes! They have a common difference of 2.)
In other words, you can express three consecutive even integers as x, (x+2), (x+4) (with a common difference of 2).
Now that you have your expressions, put them into the equation that you want. I'm assuming that it is the product of the first two plus 4 times the third is 32.
So the product of the first two is simple: multiply x and (x+2).
Then you just want to add 4 times the third: multiply 4 and (x+4)
Set all of that equal to 32. What do you get?
The equation will be x(x+2) + 4(x+4) = 32.
Simplifying what you have will give you x2+6x+16=32.
To solve this quadratic equation, it'd be best to have a zero on the right side so we can subtract 32 from both sides giving us the quadratic equation: x2+6x-16=0
When you factor, you will get (x+8)(x-2)=0 and by the zero product property, you should get your answers for x = -8 and x = 2.
Recall that we will be plugging into our consecutive even integers: x, (x+2), and (x+4).
If we are looking for our three consecutive even integers to be positive, then we we would plug in and get 2, 4, and 6. (If we are looking for negatives, then you would plug in the -8 to get three numbers -8, -6, and -4.)
Hope this helps!
