To solve the given equation, we will first simplify the expression and then apply quadratic equation methods to find the value of x.

Step 1: Simplifying the expression
The given equation is:
(x - 2)/x + 3(x + 2)/(x - 2) - 4 = 0

To simplify the equation, let's find a common denominator for the fractions. The common denominator is (x - 2) * x.

(x(x - 2) - 2 * (3(x + 2))) / (x(x - 2)) - 4 = 0
(x^2 - 2x - 6x - 12) / (x(x - 2)) - 4 = 0
(x^2 - 8x - 12) / (x(x - 2)) - 4 = 0

Step 2: Combining like terms
In the numerator, let's combine like terms:

(x^2 - 8x - 12) / (x(x - 2)) - 4 = 0
(x^2 - 8x - 12 - 4x(x - 2)) / (x(x - 2)) = 0
(x^2 - 8x - 12 - 4x^2 + 8x) / (x(x - 2)) = 0
(-3x^2 - 12) / (x(x - 2)) = 0

Step 3: Simplifying further
Let's simplify the numerator:

(-3x^2 - 12) / (x(x - 2)) = 0
-3(x^2 + 4) / (x(x - 2)) = 0

Step 4: Solving the equation
Since the equation is equal to zero, we can set each factor equal to zero and solve for x:

x^2 + 4 = 0
x^2 = -4

Since we cannot take the square root of a negative number in real numbers, there are no real solutions to this equation. Therefore, the given equation has no solution in the set of real numbers.

In summary, the given equation (x - 2)/x + 3(x + 2)/(x - 2) - 4 = 0 simplifies to -3(x^2 + 4) / (x(x - 2)) = 0 and has no real solutions.