Solve 2x^2+(m+3)x+m-1=0

$$2 x ^ { 2 } + ( m + 3 ) x + m - 1 = 0$$

Solve for m

$$m=-\frac{2x^{2}+3x-1}{x+1}$$

$$x\neq -1$$

Steps for Solving Linear Equation

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

$$2x^{2}+mx+3x+m-1=0$$

Subtract 2x^{2} from both sides. Anything subtracted from zero gives its negation.

$$mx+3x+m-1=-2x^{2}$$

Subtract 3x from both sides.

$$mx+m-1=-2x^{2}-3x$$

Add 1 to both sides.

$$mx+m=-2x^{2}-3x+1$$

Combine all terms containing m.

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

The equation is in standard form.

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

Divide both sides by x+1.

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

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

$$m=\frac{1-3x-2x^{2}}{x+1}$$

Solve for x

$$x=\frac{\sqrt{m^{2}-2m+17}-m-3}{4}$$

$$x=\frac{-\sqrt{m^{2}-2m+17}-m-3}{4}$$