Solve x*y=left(x+yright)left(y+1right)-1

$$x \times y= \left( x+y \right) \left( y+1 \right) -1$$

Solve for x

$$x=-y\left(y+1\right)+1$$

Solution Steps

Use the distributive property to multiply x+y by y+1.

$$xy=xy+x+y^{2}+y-1$$

Subtract xy from both sides.

$$xy-xy=x+y^{2}+y-1$$

Combine xy and -xy to get 0.

$$0=x+y^{2}+y-1$$

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

$$x+y^{2}+y-1=0$$

Subtract y^{2} from both sides. Anything subtracted from zero gives its negation.

$$x+y-1=-y^{2}$$

Subtract y from both sides.

$$x-1=-y^{2}-y$$

Add 1 to both sides.

$$x=-y^{2}-y+1$$

Solve for y (complex solution)

$$y=\frac{-\sqrt{5-4x}-1}{2}$$

$$y=\frac{\sqrt{5-4x}-1}{2}$$

Solve for y

$$y=\frac{-\sqrt{5-4x}-1}{2}$$

$$y=\frac{\sqrt{5-4x}-1}{2}\text{, }x\leq \frac{5}{4}$$