Solve x^2+(p-3)n+b=0

$$x ^ { 2 } + ( p - 3 ) n + b = 0$$

Solve for n (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply p-3 by n.

$$x^{2}+pn-3n+b=0$$

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

$$pn-3n+b=-x^{2}$$

Subtract b from both sides.

$$pn-3n=-x^{2}-b$$

Combine all terms containing n.

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

Divide both sides by p-3.

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

Dividing by p-3 undoes the multiplication by p-3.

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

Divide -x^{2}-b by p-3.

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

Solve for b

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

Solution Steps

Use the distributive property to multiply p-3 by n.

$$x^{2}+pn-3n+b=0$$

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

$$pn-3n+b=-x^{2}$$

Subtract pn from both sides.

$$-3n+b=-x^{2}-pn$$

Add 3n to both sides.

$$b=-x^{2}-pn+3n$$

Solve for n

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

Steps for Solving Linear Equation

Use the distributive property to multiply p-3 by n.

$$x^{2}+pn-3n+b=0$$

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

$$pn-3n+b=-x^{2}$$

Subtract b from both sides.

$$pn-3n=-x^{2}-b$$

Combine all terms containing n.

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

Divide both sides by p-3.

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

Dividing by p-3 undoes the multiplication by p-3.

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

Divide -x^{2}-b by p-3.

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