Solve nx^2+mz+y=0

$$n x ^ { 2 } + m z + y = 0$$

Solve for m

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

Steps for Solving Linear Equation

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

$$mz+y=-nx^{2}$$

Subtract y from both sides.

$$mz=-nx^{2}-y$$

The equation is in standard form.

$$zm=-nx^{2}-y$$

Divide both sides by z.

$$\frac{zm}{z}=\frac{-nx^{2}-y}{z}$$

Dividing by z undoes the multiplication by z.

$$m=\frac{-nx^{2}-y}{z}$$

Divide -nx^{2}-y by z.

$$m=-\frac{nx^{2}+y}{z}$$

Solve for n

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

Steps for Solving Linear Equation

Subtract mz from both sides. Anything subtracted from zero gives its negation.

$$nx^{2}+y=-mz$$

Subtract y from both sides.

$$nx^{2}=-mz-y$$

Reorder the terms.

$$nx^{2}=-y-mz$$

The equation is in standard form.

$$x^{2}n=-y-mz$$

Divide both sides by x^{2}.

$$\frac{x^{2}n}{x^{2}}=\frac{-y-mz}{x^{2}}$$

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

$$n=\frac{-y-mz}{x^{2}}$$

Divide -y-mz by x^{2}.

$$n=-\frac{y+mz}{x^{2}}$$