Basic Math Examples

$9 y^{2} - y^{5} = 0$

Step 1

Factor $y^{2}$ out of $9 y^{2} - y^{5}$ .

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Step 1.1

Factor $y^{2}$ out of $9 y^{2}$ .

$y^{2} \cdot 9 - y^{5} = 0$

Step 1.2

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

$y^{2} \cdot 9 + y^{2} (- y^{3}) = 0$

Step 1.3

Factor $y^{2}$ out of $y^{2} \cdot 9 + y^{2} (- y^{3})$ .

$y^{2} (9 - y^{3}) = 0$

Step 2

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

$y^{2} = 0$

$9 - y^{3} = 0$

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 $9 - y^{3}$ equal to $0$ and solve for $y$ .

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Step 4.1

Set $9 - y^{3}$ equal to $0$ .

$9 - y^{3} = 0$

Step 4.2

Solve $9 - y^{3} = 0$ for $y$ .

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Step 4.2.1

Subtract $9$ from both sides of the equation.

$- y^{3} = - 9$

Step 4.2.2

Divide each term in $- y^{3} = - 9$ by $- 1$ and simplify.

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Step 4.2.2.1

Divide each term in $- y^{3} = - 9$ by $- 1$ .

$\frac{- y^{3}}{- 1} = \frac{- 9}{- 1}$

Step 4.2.2.2

Simplify the left side.

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Step 4.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{y^{3}}{1} = \frac{- 9}{- 1}$

Step 4.2.2.2.2

Divide $y^{3}$ by $1$ .

$y^{3} = \frac{- 9}{- 1}$

Step 4.2.2.3

Simplify the right side.

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Step 4.2.2.3.1

Divide $- 9$ by $- 1$ .

$y^{3} = 9$

Step 4.2.3

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

$y = \sqrt[3]{9}$

Step 5

The final solution is all the values that make $y^{2} (9 - y^{3}) = 0$ true.

$y = 0, \sqrt[3]{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = 0, \sqrt[3]{9}$

Decimal Form:

$y = 0, 2.08008382 \dots$