Solve n-5x^2-3x+12whenx=-3

$$n - 5 x ^ { 2 } - 3 x + 12 w h e n x = - 3$$

Solve for h

$$\left\{\begin{matrix}h=-\frac{3+n-3x-5x^{2}}{12enwx}\text{, }&x\neq 0\text{ and }n\neq 0\text{ and }w\neq 0\\h\in \mathrm{R}\text{, }&\left(n=5x^{2}+3x-3\text{ and }w=0\right)\text{ or }\left(n=0\text{ and }x=\frac{-\sqrt{69}-3}{10}\right)\text{ or }\left(n=0\text{ and }x=\frac{\sqrt{69}-3}{10}\right)\text{ or }\left(n=-3\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract n from both sides.

$$-5x^{2}-3x+12whenx=-3-n$$

Add 5x^{2} to both sides.

$$-3x+12whenx=-3-n+5x^{2}$$

Add 3x to both sides.

$$12whenx=-3-n+5x^{2}+3x$$

The equation is in standard form.

$$12enwxh=5x^{2}+3x-n-3$$

Divide both sides by 12wenx.

$$\frac{12enwxh}{12enwx}=\frac{5x^{2}+3x-n-3}{12enwx}$$

Dividing by 12wenx undoes the multiplication by 12wenx.

$$h=\frac{5x^{2}+3x-n-3}{12enwx}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{3-3x-5x^{2}}{12ehwx+1}\text{, }&h=0\text{ or }w=0\text{ or }x\neq -\frac{1}{12ehw}\\n\in \mathrm{R}\text{, }&\left(x=\frac{-\sqrt{69}-3}{10}\text{ and }w=-\frac{3-\sqrt{69}}{72eh}\text{ and }h\neq 0\right)\text{ or }\left(x=\frac{\sqrt{69}-3}{10}\text{ and }w=-\frac{\sqrt{69}+3}{72eh}\text{ and }h\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 5x^{2} to both sides.

$$n-3x+12whenx=-3+5x^{2}$$

Add 3x to both sides.

$$n+12whenx=-3+5x^{2}+3x$$

Combine all terms containing n.

$$\left(1+12whex\right)n=-3+5x^{2}+3x$$

The equation is in standard form.

$$\left(12ehwx+1\right)n=5x^{2}+3x-3$$

Divide both sides by 1+12whex.

$$\frac{\left(12ehwx+1\right)n}{12ehwx+1}=\frac{5x^{2}+3x-3}{12ehwx+1}$$

Dividing by 1+12whex undoes the multiplication by 1+12whex.

$$n=\frac{5x^{2}+3x-3}{12ehwx+1}$$