Solve y=x-xUleft(x-3right)

$$y = x-xU \left( x-3 \right)$$

Solve for U (complex solution)

$$\left\{\begin{matrix}U=-\frac{x-y}{x\left(3-x\right)}\text{, }&x\neq 3\text{ and }x\neq 0\\U\in \mathrm{C}\text{, }&\left(y=0\text{ and }x=0\right)\text{ or }\left(y=3\text{ and }x=3\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply xU by x-3.

$$y=x-\left(Ux^{2}-3xU\right)$$

To find the opposite of Ux^{2}-3xU, find the opposite of each term.

$$y=x-Ux^{2}+3xU$$

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

$$x-Ux^{2}+3xU=y$$

Subtract x from both sides.

$$-Ux^{2}+3xU=y-x$$

Combine all terms containing U.

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

The equation is in standard form.

$$\left(3x-x^{2}\right)U=y-x$$

Divide both sides by -x^{2}+3x.

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

Dividing by -x^{2}+3x undoes the multiplication by -x^{2}+3x.

$$U=\frac{y-x}{3x-x^{2}}$$

Divide y-x by -x^{2}+3x.

$$U=\frac{y-x}{x\left(3-x\right)}$$

Solve for U

$$\left\{\begin{matrix}U=-\frac{x-y}{x\left(3-x\right)}\text{, }&x\neq 3\text{ and }x\neq 0\\U\in \mathrm{R}\text{, }&\left(y=0\text{ and }x=0\right)\text{ or }\left(y=3\text{ and }x=3\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply xU by x-3.

$$y=x-\left(Ux^{2}-3xU\right)$$

To find the opposite of Ux^{2}-3xU, find the opposite of each term.

$$y=x-Ux^{2}+3xU$$

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

$$x-Ux^{2}+3xU=y$$

Subtract x from both sides.

$$-Ux^{2}+3xU=y-x$$

Combine all terms containing U.

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

The equation is in standard form.

$$\left(3x-x^{2}\right)U=y-x$$

Divide both sides by -x^{2}+3x.

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

Dividing by -x^{2}+3x undoes the multiplication by -x^{2}+3x.

$$U=\frac{y-x}{3x-x^{2}}$$

Divide y-x by -x^{2}+3x.

$$U=\frac{y-x}{x\left(3-x\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{1+6U+9U^{2}-4Uy}+3U+1}{2U}\text{; }x=\frac{-\sqrt{1+6U+9U^{2}-4Uy}+3U+1}{2U}\text{, }&U\neq 0\\x=y\text{, }&U=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{1+6U+9U^{2}-4Uy}+3U+1}{2U}\text{; }x=\frac{-\sqrt{1+6U+9U^{2}-4Uy}+3U+1}{2U}\text{, }&\left(U<0\text{ or }y\leq \frac{\left(3U+1\right)^{2}}{4U}\right)\text{ and }\left(y\leq \text{Indeterminate}\text{ or }U\neq 0\right)\text{ and }\left(U>0\text{ or }\left(U\neq 0\text{ and }y\geq \frac{\left(3U+1\right)^{2}}{4U}\right)\right)\\x=y\text{, }&U=0\end{matrix}\right.$$