Solve for n -9n^2+6=-30

$- 9 n^{2} + 6 = - 30$

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

Subtract $6$ from both sides of the equation.

$- 9 n^{2} = - 30 - 6$

Subtract $6$ from $- 30$ .

$- 9 n^{2} = - 36$

Divide each term in $- 9 n^{2} = - 36$ by $- 9$ and simplify.

Divide each term in $- 9 n^{2} = - 36$ by $- 9$ .

$\frac{- 9 n^{2}}{- 9} = \frac{- 36}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 n^{2}}{- 9} = \frac{- 36}{- 9}$

Divide $n^{2}$ by $1$ .

$n^{2} = \frac{- 36}{- 9}$

Simplify the right side.

Divide $- 36$ by $- 9$ .

$n^{2} = 4$

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

$n = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$n = \pm \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$n = \pm 2$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$n = 2$

Next, use the negative value of the $\pm$ to find the second solution.

$n = - 2$

The complete solution is the result of both the positive and negative portions of the solution.

$n = 2, - 2$