Solve x^2-2(m-1)x-6m-2=-x-2

$$x ^ { 2 } - 2 ( m - 1 ) x - 6 m - 2 = - x - 2$$

Solve for m (complex solution)

$$\left\{\begin{matrix}\\m=\frac{x}{2}\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&x=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 2 to both sides.

$$x^{2}-2\left(m-1\right)x-6m=-x-2+2$$

Add -2 and 2 to get 0.

$$x^{2}-2\left(m-1\right)x-6m=-x$$

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

$$x^{2}+\left(-2m+2\right)x-6m=-x$$

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

$$x^{2}-2mx+2x-6m=-x$$

Subtract x^{2} from both sides.

$$-2mx+2x-6m=-x-x^{2}$$

Subtract 2x from both sides.

$$-2mx-6m=-x-x^{2}-2x$$

Combine -x and -2x to get -3x.

$$-2mx-6m=-3x-x^{2}$$

Combine all terms containing m.

$$\left(-2x-6\right)m=-3x-x^{2}$$

The equation is in standard form.

$$\left(-2x-6\right)m=-x^{2}-3x$$

Divide both sides by -2x-6.

$$\frac{\left(-2x-6\right)m}{-2x-6}=-\frac{x\left(x+3\right)}{-2x-6}$$

Dividing by -2x-6 undoes the multiplication by -2x-6.

$$m=-\frac{x\left(x+3\right)}{-2x-6}$$

Divide -x\left(3+x\right) by -2x-6.

$$m=\frac{x}{2}$$

Solve for m

$$\left\{\begin{matrix}\\m=\frac{x}{2}\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }&x=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 2 to both sides.

$$x^{2}-2\left(m-1\right)x-6m=-x-2+2$$

Add -2 and 2 to get 0.

$$x^{2}-2\left(m-1\right)x-6m=-x$$

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

$$x^{2}+\left(-2m+2\right)x-6m=-x$$

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

$$x^{2}-2mx+2x-6m=-x$$

Subtract x^{2} from both sides.

$$-2mx+2x-6m=-x-x^{2}$$

Subtract 2x from both sides.

$$-2mx-6m=-x-x^{2}-2x$$

Combine -x and -2x to get -3x.

$$-2mx-6m=-3x-x^{2}$$

Combine all terms containing m.

$$\left(-2x-6\right)m=-3x-x^{2}$$

The equation is in standard form.

$$\left(-2x-6\right)m=-x^{2}-3x$$

Divide both sides by -2x-6.

$$\frac{\left(-2x-6\right)m}{-2x-6}=-\frac{x\left(x+3\right)}{-2x-6}$$

Dividing by -2x-6 undoes the multiplication by -2x-6.

$$m=-\frac{x\left(x+3\right)}{-2x-6}$$

Divide -x\left(3+x\right) by -2x-6.

$$m=\frac{x}{2}$$

Solve for x

$$x=2m$$

$$x=-3$$