Basic Math Examples

$y^{2} \cdot (15 y) + 30 = 0$

Step 1

Simplify each term.

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Step 1.1

Rewrite using the commutative property of multiplication.

$15 y^{2} y + 30 = 0$

Step 1.2

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 1.2.1

Move $y$ .

$15 (y \cdot y^{2}) + 30 = 0$

Step 1.2.2

Multiply $y$ by $y^{2}$ .

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Step 1.2.2.1

Raise $y$ to the power of $1$ .

$15 (y^{1} y^{2}) + 30 = 0$

Step 1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$15 y^{1 + 2} + 30 = 0$

Step 1.2.3

Add $1$ and $2$ .

$15 y^{3} + 30 = 0$

Step 2

Subtract $30$ from both sides of the equation.

$15 y^{3} = - 30$

Step 3

Add $30$ to both sides of the equation.

$15 y^{3} + 30 = 0$

Step 4

Factor $15$ out of $15 y^{3} + 30$ .

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Step 4.1

Factor $15$ out of $15 y^{3}$ .

$15 (y^{3}) + 30 = 0$

Step 4.2

Factor $15$ out of $30$ .

$15 y^{3} + 15 \cdot 2 = 0$

Step 4.3

Factor $15$ out of $15 y^{3} + 15 \cdot 2$ .

$15 (y^{3} + 2) = 0$

Step 5

Divide each term in $15 (y^{3} + 2) = 0$ by $15$ and simplify.

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Step 5.1

Divide each term in $15 (y^{3} + 2) = 0$ by $15$ .

$\frac{15 (y^{3} + 2)}{15} = \frac{0}{15}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $15$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{15 (y^{3} + 2)}{15} = \frac{0}{15}$

Step 5.2.1.2

Divide $y^{3} + 2$ by $1$ .

$y^{3} + 2 = \frac{0}{15}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $15$ .

$y^{3} + 2 = 0$

Step 6

Subtract $2$ from both sides of the equation.

$y^{3} = - 2$

Step 7

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

$y = \sqrt[3]{- 2}$

Step 8

Simplify $\sqrt[3]{- 2}$ .

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Step 8.1

Rewrite $- 2$ as ${(- 1)}^{3} \cdot 2$ .

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Step 8.1.1

Rewrite $- 2$ as $- 1 (2)$ .

$y = \sqrt[3]{- 1 (2)}$

Step 8.1.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$y = \sqrt[3]{{(- 1)}^{3} \cdot 2}$

Step 8.2

Pull terms out from under the radical.

$y = - 1 \sqrt[3]{2}$

Step 8.3

Rewrite $- 1 \sqrt[3]{2}$ as $- \sqrt[3]{2}$ .

$y = - \sqrt[3]{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$y = - \sqrt[3]{2}$

Decimal Form:

$y = - 1.25992104 \dots$