First, simplify the left side of the equation:

7x - 3 - 9 - 4x = 7 - x
Combine like terms:
3x - 12 = 7 - x

Next, simplify the right side of the equation:

7 - x^2 - 3 = 4 - x^2

Now set the left side equal to the right side:

3x - 12 = 4 - x^2

Now, solve for x by moving all terms to one side:

x^2 + 3x - 16 = 0

Now, factor the quadratic equation:

(x + 4)(x - 4) = 0

Therefore, x = -4 or x = 4.