|(|2х-4|-5)|=9

To solve the equation \(|(|2x-4|-5)|=9\), we will break it down step-by-step.

Step 1: Analyze the Outer Absolute Value

The equation \(|A| = 9\) implies that \(A = 9\) or \(A = -9\). Here, \(A = |2x-4|-5\).

Step 2: Set Up Two Cases

So, we have two cases to consider:

1. \(|2x - 4| - 5 = 9\)
2. \(|2x - 4| - 5 = -9\)

Case 1: \(|2x - 4| - 5 = 9\)

Add 5 to both sides:

\[ |2x - 4| = 14 \]

This leads to two subcases:

1. \(2x - 4 = 14\)
2. \(2x - 4 = -14\)

Subcase 1.1:

\[ 2x - 4 = 14 \\ 2x = 18 \\ x = 9 \]

Subcase 1.2:

\[ 2x - 4 = -14 \\ 2x = -10 \\ x = -5 \]

Case 2: \(|2x - 4| - 5 = -9\)

Add 5 to both sides:

\[ |2x - 4| = -4 \]

Since the absolute value cannot be negative, there are no solutions from this case.

Step 3: Final Solutions

The solutions from Case 1 are \(x = 9\) and \(x = -5\).

Thus, the solutions to the equation \(|(|2x-4|-5)|=9\) are:

\[ \boxed{9 \text{ and } -5} \]