Solve (2x−3)(x+9)=0

Question

(
2
𝑥
−
3
)
(
𝑥
+
9
)
=
0
using the Zero Product Property.

Enter your solutions as an integer and/or fraction.

(2 points)
x=
𝑥
=


x=
𝑥
=

Answer 1

To solve the equation \((2x - 3)(x + 9) = 0\) using the Zero Product Property, we set each factor equal to zero:

1. Set the first factor equal to zero: \[ 2x - 3 = 0 \] Solving for \(x\): \[ 2x = 3 \ x = \frac{3}{2} \]

2. Set the second factor equal to zero: \[ x + 9 = 0 \] Solving for \(x\): \[ x = -9 \]

Thus, the solutions are: \[ x = \frac{3}{2} \quad \text{and} \quad x = -9 \]

In summary:

• \(x = \frac{3}{2}\)
• \(x = -9\)