Algebra Examples

$y^{3} - 5 y^{2} = 0$

Step 1

Factor $y^{2}$ out of $y^{3} - 5 y^{2}$ .

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Step 1.1

Factor $y^{2}$ out of $y^{3}$ .

$y^{2} y - 5 y^{2} = 0$

Step 1.2

Factor $y^{2}$ out of $- 5 y^{2}$ .

$y^{2} y + y^{2} \cdot - 5 = 0$

Step 1.3

Factor $y^{2}$ out of $y^{2} y + y^{2} \cdot - 5$ .

$y^{2} (y - 5) = 0$

Step 2

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

$y^{2} = 0$

$y - 5 = 0$

Step 3

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

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Step 3.1

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

$y^{2} = 0$

Step 3.2

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

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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.

$y = \pm \sqrt{0}$

Step 3.2.2

Simplify $\pm \sqrt{0}$ .

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Step 3.2.2.1

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

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

Step 3.2.2.2

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

$y = \pm 0$

Step 3.2.2.3

Plus or minus $0$ is $0$ .

$y = 0$

Step 4

Set $y - 5$ equal to $0$ and solve for $y$ .

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Step 4.1

Set $y - 5$ equal to $0$ .

$y - 5 = 0$

Step 4.2

Add $5$ to both sides of the equation.

$y = 5$

Step 5

The final solution is all the values that make $y^{2} (y - 5) = 0$ true.

$y = 0, 5$