( x^2+3x+2 ) ( x^2+7x+2 ) = 24

To solve this equation, we first need to expand the left side of the equation:

(x^2 + 3x + 2)(x^2 + 7x + 2) = x^4 + 7x^3 + 2x^2 + 3x^3 + 21x^2 + 6x + 2x^2 + 14x + 4
= x^4 + 10x^3 + 25x^2 + 20x + 4

Now we set this equal to 24:

x^4 + 10x^3 + 25x^2 + 20x + 4 = 24

Subtracting 24 from both sides, we get:

x^4 + 10x^3 + 25x^2 + 20x - 20 = 0

Now we need to solve this equation. Unfortunately, it is a quartic equation and does not have a simple solution. We can use numerical methods or a graphing calculator to find the approximate solutions.