Solve the given equation for \( x \) \( e^{2 x+4}-e=0 \) \( x=\square \) (Simplify your answer. Type a fraction or an integer. Use a comma to separate answers as needed.)

To solve the equation \( e^{2x + 4} - e = 0 \): 1. Start by isolating the exponential term: \[ e^{2x + 4} = e \] 2. Recognize that \( e^k = e^1 \) implies \( k = 1 \) because the exponential function is one-to-one: \[ 2x + 4 = 1 \] 3. Solve for \( x \): \[ 2x = 1 - 4 \\ 2x = -3 \\ x = -\frac{3}{2} \] **Answer:** \(-\frac{3}{2}\)