Solve by Factoring 12x^3-3x^2=0

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

Step 1

Factor $3 x^{2}$ out of $12 x^{3} - 3 x^{2}$ .

Factor $3 x^{2}$ out of $12 x^{3}$ .

$3 x^{2} (4 x) - 3 x^{2} = 0$

Factor $3 x^{2}$ out of $- 3 x^{2}$ .

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

Factor $3 x^{2}$ out of $3 x^{2} (4 x) + 3 x^{2} (- 1)$ .

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

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x^{2} = 0$

$4 x - 1 = 0$

Step 3

Set $x^{2}$ equal to $0$ and solve for $x$ .

Set $x^{2}$ equal to $0$ .

$x^{2} = 0$

Solve $x^{2} = 0$ for $x$ .

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Step 4

Set $4 x - 1$ equal to $0$ and solve for $x$ .

Set $4 x - 1$ equal to $0$ .

$4 x - 1 = 0$

Solve $4 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$4 x = 1$

Divide each term in $4 x = 1$ by $4$ and simplify.

Divide each term in $4 x = 1$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

The final solution is all the values that make $3 x^{2} (4 x - 1) = 0$ true.

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

Solve by Factoring 12x^3-3x^2=0

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