Expanding the left side of the equation:

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

Expanding the right side of the equation:

8(1-x^2)(x+2) = 8(x + 2 - x^2 - 2x) = 8(-x^2 - x + 2) = -8x^2 - 8x + 16

Therefore, the equation simplifies to:

-8x^3 = -8x^2 - 8x + 16

Dividing by -8 on both sides:

x^3 = x^2 + x - 2

This is the simplified form of the given equation.