Solve for y -9y^3-9=-63

$- 9 y^{3} - 9 = - 63$

Step 1

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

Add $9$ to both sides of the equation.

$- 9 y^{3} = - 63 + 9$

Add $- 63$ and $9$ .

$- 9 y^{3} = - 54$

Step 2

Add $54$ to both sides of the equation.

$- 9 y^{3} + 54 = 0$

Step 3

Factor $- 9$ out of $- 9 y^{3} + 54$ .

Factor $- 9$ out of $54$ .

$- 9 y^{3} - 9 \cdot - 6 = 0$

Factor $- 9$ out of $- 9 (y^{3}) - 9 (- 6)$ .

$- 9 (y^{3} - 6) = 0$

Step 4

Divide each term in $- 9 (y^{3} - 6) = 0$ by $- 9$ and simplify.

Divide each term in $- 9 (y^{3} - 6) = 0$ by $- 9$ .

$\frac{- 9 (y^{3} - 6)}{- 9} = \frac{0}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 (y^{3} - 6)}{- 9} = \frac{0}{- 9}$

Divide $y^{3} - 6$ by $1$ .

$y^{3} - 6 = \frac{0}{- 9}$

Simplify the right side.

Divide $0$ by $- 9$ .

$y^{3} - 6 = 0$

Step 5

Add $6$ to both sides of the equation.

$y^{3} = 6$

Step 6

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

$y = \sqrt[3]{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = \sqrt[3]{6}$

Decimal Form:

$y = 1.81712059 \dots$