To solve the equation, we can start by simplifying the left side:

301 - 12(1 - x)^2 = -1^2022

First, let's expand the square:

301 - 12(1 - 2x + x^2) = -1^2022

Next, distribute the -12:

301 - 12 + 24x - 12x^2 = -1^2022

Combine like terms:

-12x^2 + 24x + 289 = -1^2022

Now, let's simplify the right side:

-12x^2 + 24x + 289 = 1

Rearrange the equation:

-12x^2 + 24x + 288 = 0

Divide the entire equation by -12 to simplify:

x^2 - 2x - 24 = 0

Now, we can solve this quadratic equation. We can either factor it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -2, and c = -24. Plugging these values into the formula:

x = (-(-2) ± √((-2)^2 - 4(1)(-24))) / (2(1))

Simplifying:

x = (2 ± √(4 + 96)) / 2

x = (2 ± √100) / 2

x = (2 ± 10) / 2

Now, we have two possible solutions:

x = (2 + 10) / 2 = 12 / 2 = 6

x = (2 - 10) / 2 = -8 / 2 = -4

Therefore, the solutions to the equation are x = 6 and x = -4.