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

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

Solve for c

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

$$x\neq 2e$$

Steps for Solving Linear Equation

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

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

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

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

Add 6ec to both sides.

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

Subtract 3x^{2} from both sides.

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

Combine all terms containing c.

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

The equation is in standard form.

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

Divide both sides by -3x+6e.

$$\frac{\left(6e-3x\right)c}{6e-3x}=\frac{3x\left(4e-x\right)}{6e-3x}$$

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

$$c=\frac{3x\left(4e-x\right)}{6e-3x}$$

Divide 3x\left(4e-x\right) by -3x+6e.

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

Solve for x

$$x=\frac{\sqrt{c^{2}+16e^{2}}+c+4e}{2}$$

$$x=\frac{-\sqrt{c^{2}+16e^{2}}+c+4e}{2}$$