Solve (x-y)(400+5y)=4250

$$( x - y ) ( 400 + 5 y ) = 4250$$

Solve for x

$$x=\frac{y^{2}+80y+850}{y+80}$$

$$y\neq -80$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-y by 400+5y.

$$400x+5xy-400y-5y^{2}=4250$$

Add 400y to both sides.

$$400x+5xy-5y^{2}=4250+400y$$

Add 5y^{2} to both sides.

$$400x+5xy=4250+400y+5y^{2}$$

Combine all terms containing x.

$$\left(400+5y\right)x=4250+400y+5y^{2}$$

The equation is in standard form.

$$\left(5y+400\right)x=5y^{2}+400y+4250$$

Divide both sides by 400+5y.

$$\frac{\left(5y+400\right)x}{5y+400}=\frac{5y^{2}+400y+4250}{5y+400}$$

Dividing by 400+5y undoes the multiplication by 400+5y.

$$x=\frac{5y^{2}+400y+4250}{5y+400}$$

Divide 4250+400y+5y^{2} by 400+5y.

$$x=\frac{y^{2}+80y+850}{y+80}$$

Solve for y (complex solution)

$$y=\frac{-\sqrt{x^{2}+160x+3000}+x-80}{2}$$

$$y=\frac{\sqrt{x^{2}+160x+3000}+x-80}{2}$$

Solve for y

$$y=\frac{-\sqrt{x^{2}+160x+3000}+x-80}{2}$$

$$y=\frac{\sqrt{x^{2}+160x+3000}+x-80}{2}\text{, }x\geq 10\sqrt{34}-80\text{ or }x\leq -10\sqrt{34}-80$$