(3х+6)(9-х)=0

To solve the equation \((3x + 6)(9 - x) = 0\), 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.

So, we set each factor equal to zero:

1. \(3x + 6 = 0\)
2. \(9 - x = 0\)

Now we can solve each equation:

1. For \(3x + 6 = 0\): \[ 3x = -6 \\ x = -2 \]

2. For \(9 - x = 0\): \[ x = 9 \]

Thus, the solutions to the equation \((3x + 6)(9 - x) = 0\) are: \[ x = -2 \quad \text{and} \quad x = 9 \]