To solve the given equation, we need to expand and simplify the equation:

(x^2 - 1)(x + 3)(x + 5) = 20

Expanding the left side of the equation:

= (x^2 - 1)((x + 3)(x + 5))
= (x^2 - 1)(x^2 + 8x + 15)
= x^4 + 8x^3 + 15x^2 - x^2 - 8x - 15
= x^4 + 8x^3 + 14x^2 - 8x - 15

Now, we can set this expression equal to 20:

x^4 + 8x^3 + 14x^2 - 8x - 15 = 20

Rearranging the terms:

x^4 + 8x^3 + 14x^2 - 8x - 35 = 0

Now, there is no simple method to solve this quartic equation. We can solve it using numerical methods or approximation techniques.