Let's solve the given equation step by step:

12 - (1 - 6x)x = 3x(2x(2x - 1) + 2x)

First, distribute the x term inside the parentheses on the left side:
12 - x + 6x^2 = 3x(2x(2x - 1) + 2x)

Next, simplify the expression inside the parentheses on the right side:
12 - x + 6x^2 = 3x(4x^2 - 2x + 2x)

Combine like terms on the right side:
12 - x + 6x^2 = 3x(4x^2)

Now distribute 3x on the right side:
12 - x + 6x^2 = 12x^3

Rearrange the terms to set the equation to zero:
12x^3 - 6x^2 - x + 12 = 0

This is the simplified form of the given equation.