Question

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

Explanation:

Step1: Apply zero - product property

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

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

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

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

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

Answer:

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