Solve x^2(1-x+y)+x-xdy=0

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

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{1+x+xy-x^{2}}{y}\text{, }&y\neq 0\\d\in \mathrm{C}\text{, }&x=0\text{ or }\left(x=\frac{1-\sqrt{5}}{2}\text{ and }y=0\right)\text{ or }\left(x=\frac{\sqrt{5}+1}{2}\text{ and }y=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x^{2} by 1-x+y.

$$x^{2}-x^{3}+x^{2}y+x-xdy=0$$

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

$$-x^{3}+x^{2}y+x-xdy=-x^{2}$$

Add x^{3} to both sides.

$$x^{2}y+x-xdy=-x^{2}+x^{3}$$

Subtract x^{2}y from both sides.

$$x-xdy=-x^{2}+x^{3}-x^{2}y$$

Subtract x from both sides.

$$-xdy=-x^{2}+x^{3}-x^{2}y-x$$

The equation is in standard form.

$$\left(-xy\right)d=x^{3}-x^{2}-x-yx^{2}$$

Divide both sides by -xy.

$$\frac{\left(-xy\right)d}{-xy}=\frac{x\left(x^{2}-xy-x-1\right)}{-xy}$$

Dividing by -xy undoes the multiplication by -xy.

$$d=\frac{x\left(x^{2}-xy-x-1\right)}{-xy}$$

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

$$d=\frac{1+x-x^{2}}{y}+x$$

Solve for d

$$\left\{\begin{matrix}d=\frac{1+x+xy-x^{2}}{y}\text{, }&y\neq 0\\d\in \mathrm{R}\text{, }&x=0\text{ or }\left(x=\frac{1-\sqrt{5}}{2}\text{ and }y=0\right)\text{ or }\left(x=\frac{\sqrt{5}+1}{2}\text{ and }y=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x^{2} by 1-x+y.

$$x^{2}-x^{3}+x^{2}y+x-xdy=0$$

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

$$-x^{3}+x^{2}y+x-xdy=-x^{2}$$

Add x^{3} to both sides.

$$x^{2}y+x-xdy=-x^{2}+x^{3}$$

Subtract x^{2}y from both sides.

$$x-xdy=-x^{2}+x^{3}-x^{2}y$$

Subtract x from both sides.

$$-xdy=-x^{2}+x^{3}-x^{2}y-x$$

The equation is in standard form.

$$\left(-xy\right)d=x^{3}-x^{2}-x-yx^{2}$$

Divide both sides by -xy.

$$\frac{\left(-xy\right)d}{-xy}=\frac{x\left(x^{2}-xy-x-1\right)}{-xy}$$

Dividing by -xy undoes the multiplication by -xy.

$$d=\frac{x\left(x^{2}-xy-x-1\right)}{-xy}$$

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

$$d=\frac{1+x-x^{2}}{y}+x$$

Solve for x (complex solution)

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

$$x=0$$

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

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{-\sqrt{y^{2}-4dy+2y+5}+y+1}{2}\text{; }x=\frac{\sqrt{y^{2}-4dy+2y+5}+y+1}{2}\text{, }&\left(d>\frac{1-\sqrt{5}}{2}\text{ and }d<\frac{\sqrt{5}+1}{2}\right)\text{ or }y\geq \sqrt{\left(1-2d\right)^{2}-5}+2d-1\text{ or }y\leq -\sqrt{\left(1-2d\right)^{2}-5}+2d-1\text{ or }\left(d\geq \frac{1-\sqrt{5}}{2}\text{ and }d\leq \frac{\sqrt{5}+1}{2}\right)\end{matrix}\right.$$