Solve mx^2-3x-n=0

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

Solve for m (complex solution)

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

Steps for Solving Linear Equation

Add 3x to both sides. Anything plus zero gives itself.

$$mx^{2}-n=3x$$

Add n to both sides.

$$mx^{2}=3x+n$$

The equation is in standard form.

$$x^{2}m=3x+n$$

Divide both sides by x^{2}.

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

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

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

Solve for m

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

Steps for Solving Linear Equation

Add 3x to both sides. Anything plus zero gives itself.

$$mx^{2}-n=3x$$

Add n to both sides.

$$mx^{2}=3x+n$$

The equation is in standard form.

$$x^{2}m=3x+n$$

Divide both sides by x^{2}.

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

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

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

Solve for n

$$n=x\left(mx-3\right)$$

Steps for Solving Linear Equation

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

$$-3x-n=-mx^{2}$$

Add 3x to both sides.

$$-n=-mx^{2}+3x$$

The equation is in standard form.

$$-n=3x-mx^{2}$$

Divide both sides by -1.

$$\frac{-n}{-1}=\frac{x\left(3-mx\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$n=\frac{x\left(3-mx\right)}{-1}$$

Divide x\left(-mx+3\right) by -1.

$$n=mx^{2}-3x$$