To solve this equation for x, we can first rewrite both sides with the same base.

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

Rewriting the bases with a common base of 3:

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

Simplifying:

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

Now, we can rewrite the equation with the same base for both sides:

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

Using the properties of exponents, we can simplify further:

3^(x+4) / 2^(x+4) = 2 / 3^3x

Now, let's rewrite 2 / 3^3x as a fraction with a common denominator:

3^(x+4) / 2^(x+4) = 2 / 27^x

Since the bases are the same on both sides, we can equate the exponents:

x+4 = -x

2x = -4

x = -2

Therefore, the solution to the equation is x = -2.