Solve for c 4+4c^3=180

$4 + 4 c^{3} = 180$

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

Subtract $4$ from both sides of the equation.

$4 c^{3} = 180 - 4$

Subtract $4$ from $180$ .

$4 c^{3} = 176$

Subtract $176$ from both sides of the equation.

$4 c^{3} - 176 = 0$

Factor $4$ out of $4 c^{3} - 176$ .

Factor $4$ out of $4 c^{3}$ .

$4 (c^{3}) - 176 = 0$

Factor $4$ out of $- 176$ .

$4 c^{3} + 4 \cdot - 44 = 0$

Factor $4$ out of $4 c^{3} + 4 \cdot - 44$ .

$4 (c^{3} - 44) = 0$

Divide each term in $4 (c^{3} - 44) = 0$ by $4$ and simplify.

Divide each term in $4 (c^{3} - 44) = 0$ by $4$ .

$\frac{4 (c^{3} - 44)}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 (c^{3} - 44)}{4} = \frac{0}{4}$

Divide $c^{3} - 44$ by $1$ .

$c^{3} - 44 = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$c^{3} - 44 = 0$

Add $44$ to both sides of the equation.

$c^{3} = 44$

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

$c = \sqrt[3]{44}$

The result can be shown in multiple forms.

Exact Form:

$c = \sqrt[3]{44}$

Decimal Form:

$c = 3.53034833 \dots$