Solve for c 167=8c^3-9

$167 = 8 c^{3} - 9$

Rewrite the equation as $8 c^{3} - 9 = 167$ .

$8 c^{3} - 9 = 167$

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

Add $9$ to both sides of the equation.

$8 c^{3} = 167 + 9$

Add $167$ and $9$ .

$8 c^{3} = 176$

Subtract $176$ from both sides of the equation.

$8 c^{3} - 176 = 0$

Factor $8$ out of $8 c^{3} - 176$ .

Factor $8$ out of $8 c^{3}$ .

$8 (c^{3}) - 176 = 0$

Factor $8$ out of $- 176$ .

$8 c^{3} + 8 \cdot - 22 = 0$

Factor $8$ out of $8 c^{3} + 8 \cdot - 22$ .

$8 (c^{3} - 22) = 0$

Divide each term in $8 (c^{3} - 22) = 0$ by $8$ and simplify.

Divide each term in $8 (c^{3} - 22) = 0$ by $8$ .

$\frac{8 (c^{3} - 22)}{8} = \frac{0}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 (c^{3} - 22)}{8} = \frac{0}{8}$

Divide $c^{3} - 22$ by $1$ .

$c^{3} - 22 = \frac{0}{8}$

Simplify the right side.

Divide $0$ by $8$ .

$c^{3} - 22 = 0$

Add $22$ to both sides of the equation.

$c^{3} = 22$

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

$c = \sqrt[3]{22}$

The result can be shown in multiple forms.

Exact Form:

$c = \sqrt[3]{22}$

Decimal Form:

$c = 2.80203933 \dots$