Solve for n g(n)=n^2+4n

$g (n) = n^{2} + 4 n$

Since $n$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$n^{2} + 4 n = g n$

Subtract $g n$ from both sides of the equation.

$n^{2} + 4 n - g n = 0$

Factor $n$ out of $n^{2} + 4 n - g n$ .

Factor $n$ out of $n^{2}$ .

$n \cdot n + 4 n - g n = 0$

Factor $n$ out of $4 n$ .

$n \cdot n + n \cdot 4 - g n = 0$

Factor $n$ out of $- g n$ .

$n \cdot n + n \cdot 4 + n (- g) = 0$

Factor $n$ out of $n \cdot n + n \cdot 4$ .

$n (n + 4) + n (- g) = 0$

Factor $n$ out of $n (n + 4) + n (- g)$ .

$n (n + 4 - g) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$n = 0$

$n + 4 - g = 0$

Set $n$ equal to $0$ .

$n = 0$

Set $n + 4 - g$ equal to $0$ and solve for $n$ .

Set $n + 4 - g$ equal to $0$ .

$n + 4 - g = 0$

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

Subtract $4$ from both sides of the equation.

$n - g = - 4$

Add $g$ to both sides of the equation.

$n = - 4 + g$

The final solution is all the values that make $n (n + 4 - g) = 0$ true.

$n = 0$

$n = - 4 + g$