Let's first simplify the inequality:

expanding both sides of the inequality, we get:

(x^2 - 2x + 1)(x^2 - 3) ≥ (1 - 2x + x^2)(5 - 2x)

(x^4 - 3x^2 - 2x^3 + 6x + x^2 - 3) ≥ (5 - 10x + 5x^2 - 2x + 4x^2 - 2x^3)

x^4 - 3x^2 - 2x^3 + 6x + x^2 - 3 ≥ 5 - 10x + 5x^2 - 2x + 4x^2 - 2x^3

Rearranging the terms, we get:

x^4 - 2x^3 - 3x^2 + 5x + 2 ≥ 9x^2 - 12x + 5

Now, let's simplify this inequality further:

x^4 - 2x^3 - 12x^2 + 17x - 3 ≥ 0

This is the simplified form of the given inequality.

Now, we need to solve this inequality for the given condition |x| < 6. This means x can range from -6 to 6.

To solve this inequality, we can find the roots of the equation:

x^4 - 2x^3 - 12x^2 + 17x - 3 = 0

Unfortunately, this equation is quite complicated and does not seem to have an easy way to find its roots directly. You may try numeric methods or graphing to find the interval where the inequality holds true for |x| < 6.