**Solution:**

To solve the given equation, we need to simplify it and find the possible values of x.

**Step 1: Simplify the equation**
Let's simplify the given equation using the properties of exponents and algebraic operations.

2^(2x) * 3 - 3^2 * 2^x = 0

Rearranging the terms:

3 * 2^(2x) - 9 * 2^x = 0

**Step 2: Factor out the common term**
We notice that both terms have a common factor of 2^x. So, let's factor it out.

2^x * (3 * 2^x - 9) = 0

**Step 3: Solve for x**
Now, we have a product of two terms equal to zero. According to the zero product property, either one or both of the terms must be equal to zero for the equation to hold true.

Setting each factor equal to zero and solving for x:

2^x = 0 --> This equation has no solution since 2^x is always positive and can never be zero.

3 * 2^x - 9 = 0

Adding 9 to both sides of the equation:

3 * 2^x = 9

Dividing both sides of the equation by 3:

2^x = 3

**Step 4: Solve for x using logarithms**
To solve for x, we can take the logarithm of both sides of the equation. Let's use the logarithm base 2 (log2) to simplify the expression.

log2(2^x) = log2(3)

Using the property of logarithms (log base b of a^c = c * log base b of a):

x * log2(2) = log2(3)

Simplifying:

x * 1 = log2(3)

x = log2(3)

**Step 5: Approximate the value of x**
To find an approximate value for x, we can use a calculator to evaluate the logarithm of 3 base 2. The approximate value of log2(3) is 1.58496.

Therefore, the value of x is approximately 1.58496.