Solve the equation by the zero-factor property. \[ x^{2}+6 x-27=0 \]

Step 1 ：The given equation is \(x^{2}+6 x-27=0\).

Step 2 ：The zero-factor property states that if the product of two factors is zero, then at least one of the factors must be zero. To apply this property, we first need to factor the quadratic equation. The equation is in the form of \(ax^2 + bx + c = 0\). We need to find two numbers that multiply to -27 (the value of c) and add up to 6 (the value of b).

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

Step 4 ：Final Answer: The solutions to the equation are \(\boxed{x = -9}\) and \(\boxed{x = 3}\).