Solve y=y^2+10x+21/x+3

$$y = \frac { y ^ { 2 } + 10 x + 21 } { x + 3 }$$

Solve for x (complex solution)

$$x=-\frac{-y^{2}+3y-21}{y-10}$$

$$y\neq 3\text{ and }y\neq -3\text{ and }y\neq 10$$

Steps for Solving Linear Equation

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by x+3.

$$y\left(x+3\right)=y^{2}+10x+21$$

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

$$yx+3y=y^{2}+10x+21$$

Subtract 10x from both sides.

$$yx+3y-10x=y^{2}+21$$

Subtract 3y from both sides.

$$yx-10x=y^{2}+21-3y$$

Combine all terms containing x.

$$\left(y-10\right)x=y^{2}+21-3y$$

The equation is in standard form.

$$\left(y-10\right)x=y^{2}-3y+21$$

Divide both sides by y-10.

$$\frac{\left(y-10\right)x}{y-10}=\frac{y^{2}-3y+21}{y-10}$$

Dividing by y-10 undoes the multiplication by y-10.

$$x=\frac{y^{2}-3y+21}{y-10}$$

Variable x cannot be equal to -3.

$$x=\frac{y^{2}-3y+21}{y-10}\text{, }x\neq -3$$

Solve for x

$$x=-\frac{-y^{2}+3y-21}{y-10}$$

$$y\neq 10\text{ and }|y|\neq 3$$

Steps for Solving Linear Equation

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by x+3.

$$y\left(x+3\right)=y^{2}+10x+21$$

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

$$yx+3y=y^{2}+10x+21$$

Subtract 10x from both sides.

$$yx+3y-10x=y^{2}+21$$

Subtract 3y from both sides.

$$yx-10x=y^{2}+21-3y$$

Combine all terms containing x.

$$\left(y-10\right)x=y^{2}+21-3y$$

The equation is in standard form.

$$\left(y-10\right)x=y^{2}-3y+21$$

Divide both sides by y-10.

$$\frac{\left(y-10\right)x}{y-10}=\frac{y^{2}-3y+21}{y-10}$$

Dividing by y-10 undoes the multiplication by y-10.

$$x=\frac{y^{2}-3y+21}{y-10}$$

Variable x cannot be equal to -3.

$$x=\frac{y^{2}-3y+21}{y-10}\text{, }x\neq -3$$

Solve for y (complex solution)

$$y=\frac{-\sqrt{x^{2}-34x-75}+x+3}{2}$$

$$y=\frac{\sqrt{x^{2}-34x-75}+x+3}{2}\text{, }x\neq -3$$

Solve for y

$$y=\frac{-\sqrt{x^{2}-34x-75}+x+3}{2}$$

$$y=\frac{\sqrt{x^{2}-34x-75}+x+3}{2}\text{, }\left(x\leq 17-2\sqrt{91}\text{ and }x\neq -3\right)\text{ or }x\geq 2\sqrt{91}+17$$