Solve the equation by factoring. \[ x^{2}=6 x+27 \] Rewrite the equation in factored form. \[ =0 \] (Factor completely.) The solution set is (Use a comma to separate answers as needed. Type each solution only once.)

Step 1 ：The given equation is a quadratic equation. To solve it, we need to rewrite it in the standard form of a quadratic equation, which is \(ax^2 + bx + c = 0\).

Step 2 ：Rewrite the given equation \(x^{2}=6 x+27\) in the standard form: \(x^2 - 6x - 27 = 0\).

Step 3 ：Factor the quadratic equation to find the roots.

Step 4 ：The solutions to the equation are \(x = -3\) and \(x = 9\). These are the values of x that make the equation true.

Step 5 ：Final Answer: The solution set is \(\boxed{-3, 9}\).