Solve -3x(c-x)=6e(2e-c)

$$- 3 x ( c - x ) = 6 e ( 2 e - c )$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=x+2e\text{, }&x\neq 2e\\c\in \mathrm{C}\text{, }&x=2e\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-3xc+3x^{2}=6e\left(2e-c\right)$$

Use the distributive property to multiply 6e by 2e-c.

$$-3xc+3x^{2}=12e^{2}-6ec$$

Add 6ec to both sides.

$$-3xc+3x^{2}+6ec=12e^{2}$$

Subtract 3x^{2} from both sides.

$$-3xc+6ec=12e^{2}-3x^{2}$$

Combine all terms containing c.

$$\left(-3x+6e\right)c=12e^{2}-3x^{2}$$

The equation is in standard form.

$$\left(6e-3x\right)c=12e^{2}-3x^{2}$$

Divide both sides by -3x+6e.

$$\frac{\left(6e-3x\right)c}{6e-3x}=\frac{12e^{2}-3x^{2}}{6e-3x}$$

Dividing by -3x+6e undoes the multiplication by -3x+6e.

$$c=\frac{12e^{2}-3x^{2}}{6e-3x}$$

Divide 12e^{2}-3x^{2} by -3x+6e.

$$c=x+2e$$

Solve for c

$$\left\{\begin{matrix}c=x+2e\text{, }&x\neq 2e\\c\in \mathrm{R}\text{, }&x=2e\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-3xc+3x^{2}=6e\left(2e-c\right)$$

Use the distributive property to multiply 6e by 2e-c.

$$-3xc+3x^{2}=12e^{2}-6ec$$

Add 6ec to both sides.

$$-3xc+3x^{2}+6ec=12e^{2}$$

Subtract 3x^{2} from both sides.

$$-3xc+6ec=12e^{2}-3x^{2}$$

Combine all terms containing c.

$$\left(-3x+6e\right)c=12e^{2}-3x^{2}$$

The equation is in standard form.

$$\left(6e-3x\right)c=12e^{2}-3x^{2}$$

Divide both sides by -3x+6e.

$$\frac{\left(6e-3x\right)c}{6e-3x}=\frac{12e^{2}-3x^{2}}{6e-3x}$$

Dividing by -3x+6e undoes the multiplication by -3x+6e.

$$c=\frac{12e^{2}-3x^{2}}{6e-3x}$$

Divide 12e^{2}-3x^{2} by -3x+6e.

$$c=x+2e$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{\left(c-4e\right)^{2}}+c}{2}$$

$$x=\frac{\sqrt{\left(c-4e\right)^{2}}+c}{2}$$

Solve for x

$$x=c-2e$$

$$x=2e$$