Solve for n 165=6n^3+9

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

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

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

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

Subtract $9$ from both sides of the equation.

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

Subtract $9$ from $165$ .

$6 n^{3} = 156$

Subtract $156$ from both sides of the equation.

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

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

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

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

Factor $6$ out of $- 156$ .

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

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $0$ by $6$ .

$n^{3} - 26 = 0$

Add $26$ to both sides of the equation.

$n^{3} = 26$

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$n = 2.96249606 \dots$