Question

which value of x is a solution to (2x - 10)(3x + 12) = 0?

x = -36

x = -20

x = -5

x = -4

Explanation:

Step1: Apply Zero-Product Property

If \((a)(b) = 0\), then \(a = 0\) or \(b = 0\). So for \((2x - 10)(3x + 12)=0\), we have two equations:

1. \(2x - 10 = 0\)
2. \(3x + 12 = 0\)

Step2: Solve \(2x - 10 = 0\)

Add 10 to both sides: \(2x = 10\)
Divide by 2: \(x = 5\) (not among options)

Step3: Solve \(3x + 12 = 0\)

Subtract 12 from both sides: \(3x = -12\)
Divide by 3: \(x = -4\)

Answer:

\(x = -4\) (the option with \(x = -4\))