Solve for \( x \). \[ 6^{x^{2}+28 x+55}=36^{6 x-4} \] If there is more than one solution, separate them with com \( x= \)

To solve the equation \[ 6^{x^{2}+28 x+55}=36^{6 x-4}, \] we start by rewriting \(36\) in terms of \(6\): \[ 36 = 6^2. \] Thus, we can write \(36^{6x-4}\) as \((6^2)^{6x-4} = 6^{2(6x-4)} = 6^{12x-8}\). Now our equation becomes: \[ 6^{x^2 + 28x + 55} = 6^{12x - 8}. \] Since the bases are the same, we can set the exponents equal to each other: \[ x^2 + 28x + 55 = 12x - 8. \] Next, we rearrange the equation by moving all terms to one side: \[ x^2 + 28x - 12x + 55 + 8 = 0, \] which simplifies to: \[ x^2 + 16x + 63 = 0. \] Now we can factor this quadratic expression: \[ (x + 7)(x + 9) = 0. \] Setting each factor equal to zero gives us: \[ x + 7 = 0 \quad \Rightarrow \quad x = -7, \] \[ x + 9 = 0 \quad \Rightarrow \quad x = -9. \] Thus, the solutions are: \[ x = -7, -9. \] Therefore, the final answer is: \[ x = -7, -9. \]