(x-5)(18-2x)=0

To solve the equation \((x - 5)(18 - 2x) = 0\), we can use the property that if the product of two factors is zero, then at least one of the factors must be zero.

So we set each factor to zero:

1. \(x - 5 = 0\)
2. \(18 - 2x = 0\)

Now we solve each equation individually:

1. From \(x - 5 = 0\): \[ x = 5 \]

2. From \(18 - 2x = 0\): \[ 2x = 18 \\ x = \frac{18}{2} \\ x = 9 \]

Thus, the solutions to the equation \((x - 5)(18 - 2x) = 0\) are: \[ x = 5 \quad \text{and} \quad x = 9 \]