Expanding the left side of the equation:

(x+2)(x+12)(x+3)(x+8) = (x^2 + 14x + 24)(x^2 + 11x + 24)
= x^4 + 11x^3 + 24x^2 + 14x^3 + 154x^2 + 336x + 24x^2 + 264x + 576
= x^4 + 25x^3 + 242x^2 + 600x + 576

Set this equal to 4x^2:

x^4 + 25x^3 + 242x^2 + 600x + 576 = 4x^2

Rearranging terms:

x^4 + 25x^3 + 242x^2 + 600x + 576 - 4x^2 = 0
x^4 + 25x^3 + 238x^2 + 600x + 576 = 0

This is the expanded form of the given equation.