To solve the equation, we can follow these steps:

1. Distribute the exponent to the terms inside the parentheses:
109 - 7(3 - x)^2 = -3

2. Simplify the expression inside the parentheses:
109 - 7(9 - 6x + x^2) = -3

3. Distribute the 7 to each term inside the parentheses:
109 - 63 + 42x - 7x^2 = -3

4. Combine like terms:
-7x^2 + 42x + 46 = -3

5. Move all terms to one side of the equation to set it equal to zero:
-7x^2 + 42x + 46 + 3 = 0

-7x^2 + 42x + 49 = 0

6. Divide the entire equation by -7 to simplify the equation:
x^2 - 6x - 7 = 0

7. Factor the quadratic equation:
(x - 7)(x + 1) = 0

8. Set each factor equal to zero and solve for x:
x - 7 = 0 or x + 1 = 0

x = 7 or x = -1

Therefore, the solutions to the equation are x = 7 and x = -1.