To solve this equation for x, we can first simplify the terms on the left side of the equation:

229^(x-1) - 1/33^(x+3) + 1/3*3^(x+2) = 4

We know that 9 = 3^2, so we can rewrite the first term as:

223^(2(x-1)) = 223^(2x-2) = 22*9^x

Now, let's simplify the second and third terms:

1/33^(x+3) + 1/33^(x+2)
= - 1/3 3 3^(x+2) + 1/3 3^2 3^x
= -3^(x+2) + 3^(x+2)
= 0

So our equation simplifies to:

22*9^x = 4

Dividing both sides by 22:

9^x = 4/22
9^x = 2/11

Now we need to solve for x. Since 9 = 3^2, we can rewrite the equation as:

(3^2)^x = 2/11
3^2x = 2/11

3^2x = 2/11

Taking the natural logarithm of both sides:

2x * ln(3) = ln(2/11)

2x = ln(2/11) / ln(3)
x = (ln(2/11) / ln(3)) / 2

Therefore, x ≈ -1.227981.