Final answer:
The equation provided does not yield real-number solutions for n, therefore, there are no three consecutive integers that satisfy the given equation.
Step-by-step explanation:
The question is asking to find three consecutive integers that satisfy a given equation. The equation provided can be simplified as follows:
n(n+1)+(n+2)=-20-4 simplifies to n^2 + n + n + 2 = -24, which further simplifies to n^2 + 2n + 2 = -24. To solve for n, we can move all terms to one side to get n^2 + 2n + 26 = 0.
However, after simplifying, we notice that the equation n^2 + 2n + 26 = 0 does not have real solutions because the discriminant (b^2 - 4ac) is negative, and therefore the equation has no real-number solutions. Thus, there are no three consecutive integers that satisfy the equation as stated.