Let's first simplify the left side of the equation:

(4x + 1) * (2x - 4) - 8x
= 8x^2 - 16x + 2x - 4 - 8x
= 8x^2 - 22x - 4 - 8x
= 8x^2 - 30x - 4

Now let's simplify the right side of the equation:

3 * (6 - x)
= 18 - 3x

Now our equation becomes:

8x^2 - 30x - 4 = 18 - 3x

Now, we need to set the equation equal to 0:

8x^2 - 30x - 4 - 18 + 3x = 0
8x^2 - 27x - 22 = 0

This is now a quadratic equation that can be factored or solved using the quadratic formula. Let's solve it using the quadratic formula:

x = (-(-27) ± √((-27)^2 - 48(-22))) / 2*8
x = (27 ± √(729 + 704)) / 16
x = (27 ± √1433) / 16

So the solutions for x are:

x = (27 + √1433) / 16 or x = (27 - √1433) / 16