Solve A=x^2-2(m-1)x-2m+1

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

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{x^{2}+2x-A+1}{2\left(x+1\right)}\text{, }&x\neq -1\\m\in \mathrm{C}\text{, }&A=0\text{ and }x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

Subtract 1 from both sides.

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

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

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

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

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

Subtract x^{2} from both sides.

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

Subtract 2x from both sides.

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

Combine all terms containing m.

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

The equation is in standard form.

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

Divide both sides by -2x-2.

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

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

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

Divide A-\left(x+1\right)^{2} by -2x-2.

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

Solve for A

$$A=\left(x+1\right)\left(x-2m+1\right)$$

Solution Steps

Multiply -1 and 2 to get -2.

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

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

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

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

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

Solve for m

$$\left\{\begin{matrix}m=\frac{x^{2}+2x-A+1}{2\left(x+1\right)}\text{, }&x\neq -1\\m\in \mathrm{R}\text{, }&A=0\text{ and }x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

Subtract 1 from both sides.

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

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

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

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

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

Subtract x^{2} from both sides.

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

Subtract 2x from both sides.

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

Combine all terms containing m.

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

The equation is in standard form.

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

Divide both sides by -2x-2.

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

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

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

Divide A-\left(x+1\right)^{2} by -2x-2.

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