Question

1. $12x^{3}-3x^{2}=0$
2. $x$

Explanation:

Step1: Factor out common term

Factor $3x^2$ from the left side.
$3x^2(4x - 1) = 0$

Step2: Apply zero product rule

Set each factor equal to 0.
$3x^2 = 0$ or $4x - 1 = 0$

Step3: Solve for x in first equation

Isolate $x^2$, then find x.
$x^2 = 0 \implies x = 0$

Step4: Solve for x in second equation

Isolate x and simplify.
$4x = 1 \implies x = \frac{1}{4}$

Answer:

$x = 0$ (with multiplicity 2) and $x = \frac{1}{4}$