Solve nK+K=-n^2+2n+3

$$n K + K = - n ^ { 2 } + 2 n + 3$$

Solve for K

$$\left\{\begin{matrix}\\K=3-n\text{, }&\text{unconditionally}\\K\in \mathrm{R}\text{, }&n=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing K.

$$\left(n+1\right)K=-n^{2}+2n+3$$

The equation is in standard form.

$$\left(n+1\right)K=3+2n-n^{2}$$

Divide both sides by 1+n.

$$\frac{\left(n+1\right)K}{n+1}=-\frac{\left(n-3\right)\left(n+1\right)}{n+1}$$

Dividing by 1+n undoes the multiplication by 1+n.

$$K=-\frac{\left(n-3\right)\left(n+1\right)}{n+1}$$

Divide -\left(-3+n\right)\left(1+n\right) by 1+n.

$$K=3-n$$

Solve for n

$$n=-1$$

$$n=3-K$$