Solve 2mx^2-nx-3p=0

$$2 m x ^ { 2 } - n x - 3 p = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{nx+3p}{2x^{2}}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&p=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add nx to both sides. Anything plus zero gives itself.

$$2mx^{2}-3p=nx$$

Add 3p to both sides.

$$2mx^{2}=nx+3p$$

The equation is in standard form.

$$2x^{2}m=nx+3p$$

Divide both sides by 2x^{2}.

$$\frac{2x^{2}m}{2x^{2}}=\frac{nx+3p}{2x^{2}}$$

Dividing by 2x^{2} undoes the multiplication by 2x^{2}.

$$m=\frac{nx+3p}{2x^{2}}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=2mx-\frac{3p}{x}\text{, }&x\neq 0\\n\in \mathrm{C}\text{, }&p=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-nx-3p=-2mx^{2}$$

Add 3p to both sides.

$$-nx=-2mx^{2}+3p$$

The equation is in standard form.

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

Divide both sides by -x.

$$\frac{\left(-x\right)n}{-x}=\frac{3p-2mx^{2}}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$n=\frac{3p-2mx^{2}}{-x}$$

Divide -2mx^{2}+3p by -x.

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

Solve for m

$$\left\{\begin{matrix}m=\frac{nx+3p}{2x^{2}}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&p=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add nx to both sides. Anything plus zero gives itself.

$$2mx^{2}-3p=nx$$

Add 3p to both sides.

$$2mx^{2}=nx+3p$$

The equation is in standard form.

$$2x^{2}m=nx+3p$$

Divide both sides by 2x^{2}.

$$\frac{2x^{2}m}{2x^{2}}=\frac{nx+3p}{2x^{2}}$$

Dividing by 2x^{2} undoes the multiplication by 2x^{2}.

$$m=\frac{nx+3p}{2x^{2}}$$

Solve for n

$$\left\{\begin{matrix}n=2mx-\frac{3p}{x}\text{, }&x\neq 0\\n\in \mathrm{R}\text{, }&p=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-nx-3p=-2mx^{2}$$

Add 3p to both sides.

$$-nx=-2mx^{2}+3p$$

The equation is in standard form.

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

Divide both sides by -x.

$$\frac{\left(-x\right)n}{-x}=\frac{3p-2mx^{2}}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$n=\frac{3p-2mx^{2}}{-x}$$

Divide -2mx^{2}+3p by -x.

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