Solve the equation using the zero-product property \[ (x-7)(5 x+9)=0 \]

To solve the equation \((x-7)(5x+9)=0\), we can use the zero-product property, which states that if the product of two factors is zero, at least one of the factors must be zero. Setting each factor to zero gives us two equations to solve: 1. \(x - 7 = 0\) - Adding 7 to both sides, we find \(x = 7\). 2. \(5x + 9 = 0\) - Subtracting 9 from both sides results in \(5x = -9\). - Dividing by 5, we get \(x = -\frac{9}{5}\). Thus, the solutions are \(x = 7\) and \(x = -\frac{9}{5}\).