Question

solve for x. (3x + 6)(6x + 5) = 0
x = 2 or x = \frac{5}{6}
x = -2 or x = \frac{-5}{6}
x = -6 or x = -5
x = 0

Explanation:

Step1: Apply Zero-Product Property

If \((a)(b) = 0\), then \(a = 0\) or \(b = 0\). So, for \((3x + 6)(6x + 5)=0\), we set each factor equal to zero:
\(3x + 6 = 0\) or \(6x + 5 = 0\)

Step2: Solve \(3x + 6 = 0\)

Subtract 6 from both sides: \(3x = -6\)
Divide by 3: \(x = \frac{-6}{3} = -2\)

Step3: Solve \(6x + 5 = 0\)

Subtract 5 from both sides: \(6x = -5\)
Divide by 6: \(x = \frac{-5}{6}\)

Answer:

\(x = -2\) or \(x = \frac{-5}{6}\) (corresponding to the option: \(x = - 2\) or \(x = \frac{-5}{6}\))