Solve (m-2)x^2+(m+3)x-8=0

$$( m - 2 ) x ^ { 2 } + ( m + 3 ) x - 8 = 0$$

Solve for m

$$m=-\frac{-2x^{2}+3x-8}{x\left(x+1\right)}$$

$$x\neq -1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply m-2 by x^{2}.

$$mx^{2}-2x^{2}+\left(m+3\right)x-8=0$$

Use the distributive property to multiply m+3 by x.

$$mx^{2}-2x^{2}+mx+3x-8=0$$

Add 2x^{2} to both sides. Anything plus zero gives itself.

$$mx^{2}+mx+3x-8=2x^{2}$$

Subtract 3x from both sides.

$$mx^{2}+mx-8=2x^{2}-3x$$

Add 8 to both sides.

$$mx^{2}+mx=2x^{2}-3x+8$$

Combine all terms containing m.

$$\left(x^{2}+x\right)m=2x^{2}-3x+8$$

Divide both sides by x^{2}+x.

$$\frac{\left(x^{2}+x\right)m}{x^{2}+x}=\frac{2x^{2}-3x+8}{x^{2}+x}$$

Dividing by x^{2}+x undoes the multiplication by x^{2}+x.

$$m=\frac{2x^{2}-3x+8}{x^{2}+x}$$

Divide 2x^{2}-3x+8 by x^{2}+x.

$$m=\frac{2x^{2}-3x+8}{x\left(x+1\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{m^{2}+38m-55}-m-3}{2\left(m-2\right)}\text{; }x=-\frac{\sqrt{m^{2}+38m-55}+m+3}{2\left(m-2\right)}\text{, }&m\neq 2\\x=\frac{8}{5}\text{, }&m=2\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{m^{2}+38m-55}-m-3}{2\left(m-2\right)}\text{; }x=-\frac{\sqrt{m^{2}+38m-55}+m+3}{2\left(m-2\right)}\text{, }&m\leq -4\sqrt{26}-19\text{ or }\left(m\neq 2\text{ and }m\geq 4\sqrt{26}-19\right)\\x=\frac{8}{5}\text{, }&m=2\end{matrix}\right.$$