To solve the equation 2(2-x^2)(12-x^2)(22-x^2)(32-x^2)+12558=0, we can start by factoring out the common factor of (2-x^2):

(2-x^2)(12-x^2)(22-x^2)(32-x^2) + 12558 = 0

Let's substitute y = 2-x^2:

y(12-x^2)(22-x^2)(32-x^2) + 12558 = 0

Now, we can rewrite the equation as:

y(12-y)(22-y)(32-y) + 12558 = 0

Expanding the equation, we get:

y(12)(22)(32) - y(12)(22)(y) - y(12)(32)(y) - y(22)(32)(y) + y(y)(12)(22)(32) + 12558 = 0

Simplifying further:

8448y - 264y^2 - 384y^2 - 704y^2 + 8448y^3 + 12558 = 0

Combining like terms:

8448y^3 - 1352y^2 + 8448y + 12558 = 0

Now, we can solve this cubic equation for y. However, finding the exact solutions for a cubic equation can be quite complex. It is often easier to use numerical methods or a graphing calculator to approximate the solutions.