The problem is to solve the equation $12x^3 = 3x^2$ for $x$.

1. Problem Description

The problem is to solve the equation $12x^3 = 3x^2$ for $x$.

2. Solution Steps

To solve the equation $12x^3 = 3x^2$, we first rearrange the equation to get all terms on one side:

$12x^3 - 3x^2 = 0$

Next, we factor out the greatest common factor, which is $3x^2$:

$3x^2(4x - 1) = 0$

Now, we set each factor equal to zero and solve for $x$.

$3x^2 = 0$ or $4x - 1 = 0$

From $3x^2 = 0$, we get $x^2 = 0$, which implies $x = 0$.

From $4x - 1 = 0$, we get $4x = 1$, which implies $x = \frac{1}{4}$.

Thus, the solutions for $x$ are $0$ and $\frac{1}{4}$.

3. Final Answer

$x = 0, \frac{1}{4}$