Question

solve (3x - 2)(x - 4) = 0

Explanation:

Step1: Apply Zero-Product Property

If \(ab = 0\), then either \(a = 0\) or \(b = 0\). Here, \(a = 3x - 2\) and \(b = x - 4\), so we set each factor equal to zero:
\(3x - 2 = 0\) or \(x - 4 = 0\)

Step2: Solve \(3x - 2 = 0\)

Add 2 to both sides:
\(3x - 2 + 2 = 0 + 2\)
\(3x = 2\)
Divide both sides by 3:
\(x=\frac{2}{3}\)

Step3: Solve \(x - 4 = 0\)

Add 4 to both sides:
\(x - 4 + 4 = 0 + 4\)
\(x = 4\)

Answer:

\(x=\frac{2}{3}\) or \(x = 4\)