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