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

Explanation:

Step1: Apply zero-product property

If $(a)(b)=0$, then $a=0$ or $b=0$. So we set each factor equal to 0: $3x-2=0$ or $x-4=0$

Step2: Solve first equation for $x$

Isolate $x$ by adding 2 then dividing by 3: $3x=2 \implies x=\frac{2}{3}$

Step3: Solve second equation for $x$

Isolate $x$ by adding 4: $x=4$

Answer:

$x=\frac{2}{3}$ or $x=4$