Solve x^2-2yx+7=-6y+x^2+2x+1

$${ x }^{ 2 } -2yx+7=-6y+ { x }^{ 2 } +2x+1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=3\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$x^{2}-2yx+7-x^{2}=-6y+2x+1$$

Combine x^{2} and -x^{2} to get 0.

$$-2yx+7=-6y+2x+1$$

Subtract 2x from both sides.

$$-2yx+7-2x=-6y+1$$

Subtract 7 from both sides.

$$-2yx-2x=-6y+1-7$$

Subtract 7 from 1 to get -6.

$$-2yx-2x=-6y-6$$

Combine all terms containing x.

$$\left(-2y-2\right)x=-6y-6$$

Divide both sides by -2y-2.

$$\frac{\left(-2y-2\right)x}{-2y-2}=\frac{-6y-6}{-2y-2}$$

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

$$x=\frac{-6y-6}{-2y-2}$$

Divide -6y-6 by -2y-2.

$$x=3$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=-1\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 6y to both sides.

$$x^{2}-2yx+7+6y=x^{2}+2x+1$$

Subtract x^{2} from both sides.

$$-2yx+7+6y=x^{2}+2x+1-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$-2yx+7+6y=2x+1$$

Subtract 7 from both sides.

$$-2yx+6y=2x+1-7$$

Subtract 7 from 1 to get -6.

$$-2yx+6y=2x-6$$

Combine all terms containing y.

$$\left(-2x+6\right)y=2x-6$$

The equation is in standard form.

$$\left(6-2x\right)y=2x-6$$

Divide both sides by -2x+6.

$$\frac{\left(6-2x\right)y}{6-2x}=\frac{2x-6}{6-2x}$$

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

$$y=\frac{2x-6}{6-2x}$$

Divide -6+2x by -2x+6.

$$y=-1$$

Solve for x

$$\left\{\begin{matrix}\\x=3\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$x^{2}-2yx+7-x^{2}=-6y+2x+1$$

Combine x^{2} and -x^{2} to get 0.

$$-2yx+7=-6y+2x+1$$

Subtract 2x from both sides.

$$-2yx+7-2x=-6y+1$$

Subtract 7 from both sides.

$$-2yx-2x=-6y+1-7$$

Subtract 7 from 1 to get -6.

$$-2yx-2x=-6y-6$$

Combine all terms containing x.

$$\left(-2y-2\right)x=-6y-6$$

Divide both sides by -2y-2.

$$\frac{\left(-2y-2\right)x}{-2y-2}=\frac{-6y-6}{-2y-2}$$

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

$$x=\frac{-6y-6}{-2y-2}$$

Divide -6y-6 by -2y-2.

$$x=3$$

Solve for y

$$\left\{\begin{matrix}\\y=-1\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 6y to both sides.

$$x^{2}-2yx+7+6y=x^{2}+2x+1$$

Subtract x^{2} from both sides.

$$-2yx+7+6y=x^{2}+2x+1-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$-2yx+7+6y=2x+1$$

Subtract 7 from both sides.

$$-2yx+6y=2x+1-7$$

Subtract 7 from 1 to get -6.

$$-2yx+6y=2x-6$$

Combine all terms containing y.

$$\left(-2x+6\right)y=2x-6$$

The equation is in standard form.

$$\left(6-2x\right)y=2x-6$$

Divide both sides by -2x+6.

$$\frac{\left(6-2x\right)y}{6-2x}=\frac{2x-6}{6-2x}$$

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

$$y=\frac{2x-6}{6-2x}$$

Divide -6+2x by -2x+6.

$$y=-1$$