Algebra Examples

$165 = 6 n^{3} + 9$

Step 1

Rewrite the equation as $6 n^{3} + 9 = 165$ .

$6 n^{3} + 9 = 165$

Step 2

Move all terms not containing $n$ to the right side of the equation.

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Step 2.1

Subtract $9$ from both sides of the equation.

$6 n^{3} = 165 - 9$

Step 2.2

Subtract $9$ from $165$ .

$6 n^{3} = 156$

Step 3

Subtract $156$ from both sides of the equation.

$6 n^{3} - 156 = 0$

Step 4

Factor $6$ out of $6 n^{3} - 156$ .

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Step 4.1

Factor $6$ out of $6 n^{3}$ .

$6 (n^{3}) - 156 = 0$

Step 4.2

Factor $6$ out of $- 156$ .

$6 n^{3} + 6 \cdot - 26 = 0$

Step 4.3

Factor $6$ out of $6 n^{3} + 6 \cdot - 26$ .

$6 (n^{3} - 26) = 0$

Step 5

Divide each term in $6 (n^{3} - 26) = 0$ by $6$ and simplify.

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Step 5.1

Divide each term in $6 (n^{3} - 26) = 0$ by $6$ .

$\frac{6 (n^{3} - 26)}{6} = \frac{0}{6}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $6$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{6 (n^{3} - 26)}{6} = \frac{0}{6}$

Step 5.2.1.2

Divide $n^{3} - 26$ by $1$ .

$n^{3} - 26 = \frac{0}{6}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $6$ .

$n^{3} - 26 = 0$

Step 6

Add $26$ to both sides of the equation.

$n^{3} = 26$

Step 7

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

$n = \sqrt[3]{26}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$n = \sqrt[3]{26}$

Decimal Form:

$n = 2.96249606 \dots$