To solve the equation \((2x - 7)(x + 9) = 0\), we can use the zero product property. This property states that if the product of two factors equals zero, at least one of the factors must be zero.
We set each factor equal to zero:
- \(2x - 7 = 0\)
- \(x + 9 = 0\)
Now, we solve each equation individually:
-
For \(2x - 7 = 0\):
\[ 2x = 7 \] \[ x = \frac{7}{2} \] \[ x = 3.5 \]
-
For \(x + 9 = 0\):
\[ x = -9 \]
Thus, the solutions to the equation \((2x - 7)(x + 9) = 0\) are:
\[ x = \frac{7}{2} \quad \text{or} \quad x = -9 \]