Solve nx^2-12=-4p-pxh

$$n x ^ { 2 } - 12 = - 4 p - p x h$$

Solve for h (complex solution)

$$\left\{\begin{matrix}h=\frac{12-4p-nx^{2}}{px}\text{, }&x\neq 0\text{ and }p\neq 0\\h\in \mathrm{C}\text{, }&\left(p=0\text{ and }n=\frac{12}{x^{2}}\text{ and }x\neq 0\right)\text{ or }\left(p=3\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$-4p-pxh=nx^{2}-12$$

Add 4p to both sides.

$$-pxh=nx^{2}-12+4p$$

The equation is in standard form.

$$\left(-px\right)h=nx^{2}+4p-12$$

Divide both sides by -px.

$$\frac{\left(-px\right)h}{-px}=\frac{nx^{2}+4p-12}{-px}$$

Dividing by -px undoes the multiplication by -px.

$$h=\frac{nx^{2}+4p-12}{-px}$$

Divide nx^{2}-12+4p by -px.

$$h=-\frac{nx^{2}+4p-12}{px}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{hpx+4p-12}{x^{2}}\text{, }&x\neq 0\\n\in \mathrm{C}\text{, }&p=3\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 12 to both sides.

$$nx^{2}=-4p-pxh+12$$

Reorder the terms.

$$nx^{2}=-hpx-4p+12$$

The equation is in standard form.

$$x^{2}n=12-4p-hpx$$

Divide both sides by x^{2}.

$$\frac{x^{2}n}{x^{2}}=\frac{12-4p-hpx}{x^{2}}$$

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

$$n=\frac{12-4p-hpx}{x^{2}}$$

Solve for h

$$\left\{\begin{matrix}h=\frac{12-4p-nx^{2}}{px}\text{, }&x\neq 0\text{ and }p\neq 0\\h\in \mathrm{R}\text{, }&\left(p=0\text{ and }n=\frac{12}{x^{2}}\text{ and }x\neq 0\right)\text{ or }\left(p=3\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$-4p-pxh=nx^{2}-12$$

Add 4p to both sides.

$$-pxh=nx^{2}-12+4p$$

The equation is in standard form.

$$\left(-px\right)h=nx^{2}+4p-12$$

Divide both sides by -px.

$$\frac{\left(-px\right)h}{-px}=\frac{nx^{2}+4p-12}{-px}$$

Dividing by -px undoes the multiplication by -px.

$$h=\frac{nx^{2}+4p-12}{-px}$$

Divide nx^{2}-12+4p by -px.

$$h=-\frac{nx^{2}+4p-12}{px}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{hpx+4p-12}{x^{2}}\text{, }&x\neq 0\\n\in \mathrm{R}\text{, }&p=3\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 12 to both sides.

$$nx^{2}=-4p-pxh+12$$

Reorder the terms.

$$nx^{2}=-hpx-4p+12$$

The equation is in standard form.

$$x^{2}n=12-4p-hpx$$

Divide both sides by x^{2}.

$$\frac{x^{2}n}{x^{2}}=\frac{12-4p-hpx}{x^{2}}$$

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

$$n=\frac{12-4p-hpx}{x^{2}}$$