Solve (m+4)x^2-2(m-1)x-1-2m=0

$$( m + 4 ) x ^ { 2 } - 2 ( m - 1 ) x - 1 - 2 m = 0$$

Solve for m

$$m=-\frac{4x^{2}+2x-1}{x^{2}-2x-2}$$

$$x\neq \sqrt{3}+1\text{ and }x\neq 1-\sqrt{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply m+4 by x^{2}.

$$mx^{2}+4x^{2}-2\left(m-1\right)x-1-2m=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$mx^{2}+4x^{2}-2\left(m-1\right)x-2m=1$$

Use the distributive property to multiply -2 by m-1.

$$mx^{2}+4x^{2}+\left(-2m+2\right)x-2m=1$$

Use the distributive property to multiply -2m+2 by x.

$$mx^{2}+4x^{2}-2mx+2x-2m=1$$

Subtract 4x^{2} from both sides.

$$mx^{2}-2mx+2x-2m=1-4x^{2}$$

Subtract 2x from both sides.

$$mx^{2}-2mx-2m=1-4x^{2}-2x$$

Combine all terms containing m.

$$\left(x^{2}-2x-2\right)m=1-4x^{2}-2x$$

The equation is in standard form.

$$\left(x^{2}-2x-2\right)m=1-2x-4x^{2}$$

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

$$\frac{\left(x^{2}-2x-2\right)m}{x^{2}-2x-2}=\frac{1-2x-4x^{2}}{x^{2}-2x-2}$$

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

$$m=\frac{1-2x-4x^{2}}{x^{2}-2x-2}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{3m^{2}+7m+5}+m-1}{m+4}\text{; }x=\frac{-\sqrt{3m^{2}+7m+5}+m-1}{m+4}\text{, }&m\neq -4\\x=-\frac{7}{10}\text{, }&m=-4\end{matrix}\right.$$