Solve +K(s^2+2s+2)/s^2-3s+2=0

$$+ \frac { K ( s ^ { 2 } + 2 s + 2 ) } { s ^ { 2 } - 3 s + 2 } = 0$$

Solve for K (complex solution)

$$\left\{\begin{matrix}K=0\text{, }&s\neq 1\text{ and }s\neq 2\\K\in \mathrm{C}\text{, }&s=-1+i\text{ or }s=-1-i\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(s-2\right)\left(s-1\right).

$$K\left(s^{2}+2s+2\right)=0$$

Use the distributive property to multiply K by s^{2}+2s+2.

$$Ks^{2}+2Ks+2K=0$$

Combine all terms containing K.

$$\left(s^{2}+2s+2\right)K=0$$

Divide 0 by s^{2}+2s+2.

$$K=0$$

Solve for K

$$K=0$$

$$s\neq 2\text{ and }s\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(s-2\right)\left(s-1\right).

$$K\left(s^{2}+2s+2\right)=0$$

Use the distributive property to multiply K by s^{2}+2s+2.

$$Ks^{2}+2Ks+2K=0$$

Combine all terms containing K.

$$\left(s^{2}+2s+2\right)K=0$$

Divide 0 by s^{2}+2s+2.

$$K=0$$

Solve for s (complex solution)

$$\left\{\begin{matrix}\\s=-1+i\text{; }s=-1-i\text{, }&\text{unconditionally}\\s\in \mathrm{C}\setminus 1,2\text{, }&K=0\end{matrix}\right.$$

Solve for s

$$s\in \mathrm{R}\setminus 2,1$$

$$K=0$$