Solve 3(2x^2-mx)+4nx-2mn=0

$$3 ( 2 x ^ { 2 } - m x ) + 4 n x - 2 m n = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}\\m=2x\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&x=-\frac{2n}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 2x^{2}-mx.

$$6x^{2}-3xm+4nx-2mn=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-3xm+4nx-2mn=-6x^{2}$$

Subtract 4nx from both sides.

$$-3xm-2mn=-6x^{2}-4nx$$

Combine all terms containing m.

$$\left(-3x-2n\right)m=-6x^{2}-4nx$$

Divide both sides by -3x-2n.

$$\frac{\left(-3x-2n\right)m}{-3x-2n}=-\frac{2x\left(3x+2n\right)}{-3x-2n}$$

Dividing by -3x-2n undoes the multiplication by -3x-2n.

$$m=-\frac{2x\left(3x+2n\right)}{-3x-2n}$$

Divide -2x\left(3x+2n\right) by -3x-2n.

$$m=2x$$

Solve for n (complex solution)

$$\left\{\begin{matrix}\\n=-\frac{3x}{2}\text{, }&\text{unconditionally}\\n\in \mathrm{C}\text{, }&x=\frac{m}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 2x^{2}-mx.

$$6x^{2}-3mx+4nx-2mn=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-3mx+4nx-2mn=-6x^{2}$$

Add 3mx to both sides.

$$4nx-2mn=-6x^{2}+3mx$$

Combine all terms containing n.

$$\left(4x-2m\right)n=-6x^{2}+3mx$$

The equation is in standard form.

$$\left(4x-2m\right)n=3mx-6x^{2}$$

Divide both sides by 4x-2m.

$$\frac{\left(4x-2m\right)n}{4x-2m}=\frac{3x\left(m-2x\right)}{4x-2m}$$

Dividing by 4x-2m undoes the multiplication by 4x-2m.

$$n=\frac{3x\left(m-2x\right)}{4x-2m}$$

Divide 3x\left(-2x+m\right) by 4x-2m.

$$n=-\frac{3x}{2}$$

Solve for m

$$\left\{\begin{matrix}\\m=2x\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }&x=-\frac{2n}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 2x^{2}-mx.

$$6x^{2}-3xm+4nx-2mn=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-3xm+4nx-2mn=-6x^{2}$$

Subtract 4nx from both sides.

$$-3xm-2mn=-6x^{2}-4nx$$

Combine all terms containing m.

$$\left(-3x-2n\right)m=-6x^{2}-4nx$$

Divide both sides by -3x-2n.

$$\frac{\left(-3x-2n\right)m}{-3x-2n}=-\frac{2x\left(3x+2n\right)}{-3x-2n}$$

Dividing by -3x-2n undoes the multiplication by -3x-2n.

$$m=-\frac{2x\left(3x+2n\right)}{-3x-2n}$$

Divide -2x\left(3x+2n\right) by -3x-2n.

$$m=2x$$

Solve for n

$$\left\{\begin{matrix}\\n=-\frac{3x}{2}\text{, }&\text{unconditionally}\\n\in \mathrm{R}\text{, }&x=\frac{m}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 2x^{2}-mx.

$$6x^{2}-3mx+4nx-2mn=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-3mx+4nx-2mn=-6x^{2}$$

Add 3mx to both sides.

$$4nx-2mn=-6x^{2}+3mx$$

Combine all terms containing n.

$$\left(4x-2m\right)n=-6x^{2}+3mx$$

The equation is in standard form.

$$\left(4x-2m\right)n=3mx-6x^{2}$$

Divide both sides by 4x-2m.

$$\frac{\left(4x-2m\right)n}{4x-2m}=\frac{3x\left(m-2x\right)}{4x-2m}$$

Dividing by 4x-2m undoes the multiplication by 4x-2m.

$$n=\frac{3x\left(m-2x\right)}{4x-2m}$$

Divide 3x\left(-2x+m\right) by 4x-2m.

$$n=-\frac{3x}{2}$$