|2x+8| * (x-4)=0

To solve the equation \(|2x + 8| \cdot (x - 4) = 0\), we need to find the values of \(x\) that make the product equal to zero. This can occur if either factor in the product equals zero.

Step 1: Solve \( |2x + 8| = 0 \)

The absolute value \(|A| = 0\) only when \(A = 0\). Thus, we solve:

\[ 2x + 8 = 0 \]

Subtract 8 from both sides:

\[ 2x = -8 \]

Now divide by 2:

\[ x = -4 \]

Step 2: Solve \( x - 4 = 0 \)

Next, we solve the second factor:

\[ x - 4 = 0 \]

Add 4 to both sides:

\[ x = 4 \]

Step 3: Combine Solutions

The solutions to the equation \(|2x + 8| \cdot (x - 4) = 0\) are:

\[ x = -4 \quad \text{and} \quad x = 4 \]

Final Answer

The values of \(x\) that satisfy the equation are:

\[ x = -4, \quad x = 4 \]