Solve for n (n+4)^(1/2)=(-2-2n)^(1/2)

${(n + 4)}^{\frac{1}{2}} = {(- 2 - 2 n)}^{\frac{1}{2}}$

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$n + 4 = - 2 - 2 n$

Solve for $n$ .

Move all terms containing $n$ to the left side of the equation.

Add $2 n$ to both sides of the equation.

$n + 4 + 2 n = - 2$

Add $n$ and $2 n$ .

$3 n + 4 = - 2$

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

Subtract $4$ from both sides of the equation.

$3 n = - 2 - 4$

Subtract $4$ from $- 2$ .

$3 n = - 6$

Divide each term in $3 n = - 6$ by $3$ and simplify.

Divide each term in $3 n = - 6$ by $3$ .

$\frac{3 n}{3} = \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 n}{3} = \frac{- 6}{3}$

Divide $n$ by $1$ .

$n = \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

$n = - 2$