Solve the equation by the zero-factor property. \[ w^{2}-12 w+35=0 \]

Step 1 ：The given equation is a quadratic equation. The zero-factor property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can solve the equation by factoring it and setting each factor equal to zero.

Step 2 ：Factor the equation \(w^{2}-12 w+35=0\) into \((w-5)(w-7)=0\).

Step 3 ：Set each factor equal to zero and solve for w: \(w-5=0\) gives \(w=5\) and \(w-7=0\) gives \(w=7\).

Step 4 ：Final Answer: The solutions to the equation are \(\boxed{w = 5}\) and \(\boxed{w = 7}\).