Calculus Examples

$4 X^{3} - 12 X^{2} = 0$

Step 1

Factor $4 X^{2}$ out of $4 X^{3} - 12 X^{2}$ .

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Step 1.1

Factor $4 X^{2}$ out of $4 X^{3}$ .

$4 X^{2} (X) - 12 X^{2} = 0$

Step 1.2

Factor $4 X^{2}$ out of $- 12 X^{2}$ .

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

Step 1.3

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

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

Step 2

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

$X^{2} = 0$

$X - 3 = 0$

Step 3

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

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Step 3.1

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

$X^{2} = 0$

Step 3.2

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

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Step 3.2.1

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

$X = \pm \sqrt{0}$

Step 3.2.2

Simplify $\pm \sqrt{0}$ .

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Step 3.2.2.1

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

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

Step 3.2.2.2

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

$X = \pm 0$

Step 3.2.2.3

Plus or minus $0$ is $0$ .

$X = 0$

Step 4

Set $X - 3$ equal to $0$ and solve for $X$ .

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Step 4.1

Set $X - 3$ equal to $0$ .

$X - 3 = 0$

Step 4.2

Add $3$ to both sides of the equation.

$X = 3$

Step 5

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

$X = 0, 3$