Basic Math Examples

$y^{2} (y - 4) = 0$

Step 1

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

$y^{2} = 0$

$y - 4 = 0$

Step 2

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

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Step 2.1

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

$y^{2} = 0$

Step 2.2

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

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Step 2.2.1

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

$y = \pm \sqrt{0}$

Step 2.2.2

Simplify $\pm \sqrt{0}$ .

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

$y = \pm 0$

Step 2.2.2.3

Plus or minus $0$ is $0$ .

$y = 0$

Step 3

Set $y - 4$ equal to $0$ and solve for $y$ .

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Step 3.1

Set $y - 4$ equal to $0$ .

$y - 4 = 0$

Step 3.2

Add $4$ to both sides of the equation.

$y = 4$

Step 4

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

$y = 0, 4$