Use the Zero Product Property to solve (2x−5)(x+3)=0

Question

.(2 points)
x=


x=

Answer 1

To solve the equation \((2x−5)(x+3)=0\) using the Zero Product Property, we set each factor equal to zero:

1. Set the first factor equal to zero: \[ 2x - 5 = 0 \] Solving for \(x\): \[ 2x = 5 \quad \Rightarrow \quad x = \frac{5}{2} \quad \Rightarrow \quad x = 2.5 \]

2. Set the second factor equal to zero: \[ x + 3 = 0 \] Solving for \(x\): \[ x = -3 \]

Thus, the solutions are: \[ x = 2.5 \quad \text{and} \quad x = -3 \]

So, in summary:

• \(x = 2.5\)
• \(x = -3\)