Solve the given equation by the zero-factor property.
\[
64 x^{2}+48 x+9=0
\]

Step 1 ：The given equation is a quadratic equation of the form \(ax^2 + bx + c = 0\).

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.

Step 3 ：To solve the equation using the zero-factor property, we first need to factorize the equation. However, this equation does not seem to be easily factorizable.

Step 4 ：Therefore, we can use the quadratic formula to find the roots of the equation. The quadratic formula is given by: \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Step 5 ：where a, b, and c are the coefficients of the quadratic equation. In this case, a = 64, b = 48, and c = 9.

Step 6 ：Substituting these values into the quadratic formula, we get the solutions to the equation.

Step 7 ：The solutions to the equation are complex numbers. This means that the equation has no real roots.

Step 8 ：The roots are both -0.375.

Step 9 ：Final Answer: The solutions to the equation are \(\boxed{-0.375}\) and \(\boxed{-0.375}\).