Solve (n-3)x^2+(m+3)x-(m+1)=0

$$( n - 3 ) x ^ { 2 } + ( m + 3 ) x - ( m + 1 ) = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{nx^{2}-3x^{2}+3x-1}{x-1}\text{, }&x\neq 1\\m\in \mathrm{C}\text{, }&x=1\text{ and }n=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-3 by x^{2}.

$$nx^{2}-3x^{2}+\left(m+3\right)x-\left(m+1\right)=0$$

Use the distributive property to multiply m+3 by x.

$$nx^{2}-3x^{2}+mx+3x-\left(m+1\right)=0$$

To find the opposite of m+1, find the opposite of each term.

$$nx^{2}-3x^{2}+mx+3x-m-1=0$$

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

$$-3x^{2}+mx+3x-m-1=-nx^{2}$$

Add 3x^{2} to both sides.

$$mx+3x-m-1=-nx^{2}+3x^{2}$$

Subtract 3x from both sides.

$$mx-m-1=-nx^{2}+3x^{2}-3x$$

Add 1 to both sides.

$$mx-m=-nx^{2}+3x^{2}-3x+1$$

Combine all terms containing m.

$$\left(x-1\right)m=-nx^{2}+3x^{2}-3x+1$$

The equation is in standard form.

$$\left(x-1\right)m=1-3x+3x^{2}-nx^{2}$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)m}{x-1}=\frac{1-3x+3x^{2}-nx^{2}}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$m=\frac{1-3x+3x^{2}-nx^{2}}{x-1}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{-3x^{2}+mx+3x-m-1}{x^{2}}\text{, }&x\neq 0\\n\in \mathrm{C}\text{, }&m=-1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-3 by x^{2}.

$$nx^{2}-3x^{2}+\left(m+3\right)x-\left(m+1\right)=0$$

Use the distributive property to multiply m+3 by x.

$$nx^{2}-3x^{2}+mx+3x-\left(m+1\right)=0$$

To find the opposite of m+1, find the opposite of each term.

$$nx^{2}-3x^{2}+mx+3x-m-1=0$$

Add 3x^{2} to both sides. Anything plus zero gives itself.

$$nx^{2}+mx+3x-m-1=3x^{2}$$

Subtract mx from both sides.

$$nx^{2}+3x-m-1=3x^{2}-mx$$

Subtract 3x from both sides.

$$nx^{2}-m-1=3x^{2}-mx-3x$$

Add m to both sides.

$$nx^{2}-1=3x^{2}-mx-3x+m$$

Add 1 to both sides.

$$nx^{2}=3x^{2}-mx-3x+m+1$$

The equation is in standard form.

$$x^{2}n=3x^{2}-mx-3x+m+1$$

Divide both sides by x^{2}.

$$\frac{x^{2}n}{x^{2}}=\frac{3x^{2}-mx-3x+m+1}{x^{2}}$$

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

$$n=\frac{3x^{2}-mx-3x+m+1}{x^{2}}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{nx^{2}-3x^{2}+3x-1}{x-1}\text{, }&x\neq 1\\m\in \mathrm{R}\text{, }&x=1\text{ and }n=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-3 by x^{2}.

$$nx^{2}-3x^{2}+\left(m+3\right)x-\left(m+1\right)=0$$

Use the distributive property to multiply m+3 by x.

$$nx^{2}-3x^{2}+mx+3x-\left(m+1\right)=0$$

To find the opposite of m+1, find the opposite of each term.

$$nx^{2}-3x^{2}+mx+3x-m-1=0$$

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

$$-3x^{2}+mx+3x-m-1=-nx^{2}$$

Add 3x^{2} to both sides.

$$mx+3x-m-1=-nx^{2}+3x^{2}$$

Subtract 3x from both sides.

$$mx-m-1=-nx^{2}+3x^{2}-3x$$

Add 1 to both sides.

$$mx-m=-nx^{2}+3x^{2}-3x+1$$

Combine all terms containing m.

$$\left(x-1\right)m=-nx^{2}+3x^{2}-3x+1$$

The equation is in standard form.

$$\left(x-1\right)m=1-3x+3x^{2}-nx^{2}$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)m}{x-1}=\frac{1-3x+3x^{2}-nx^{2}}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$m=\frac{1-3x+3x^{2}-nx^{2}}{x-1}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{-3x^{2}+mx+3x-m-1}{x^{2}}\text{, }&x\neq 0\\n\in \mathrm{R}\text{, }&m=-1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-3 by x^{2}.

$$nx^{2}-3x^{2}+\left(m+3\right)x-\left(m+1\right)=0$$

Use the distributive property to multiply m+3 by x.

$$nx^{2}-3x^{2}+mx+3x-\left(m+1\right)=0$$

To find the opposite of m+1, find the opposite of each term.

$$nx^{2}-3x^{2}+mx+3x-m-1=0$$

Add 3x^{2} to both sides. Anything plus zero gives itself.

$$nx^{2}+mx+3x-m-1=3x^{2}$$

Subtract mx from both sides.

$$nx^{2}+3x-m-1=3x^{2}-mx$$

Subtract 3x from both sides.

$$nx^{2}-m-1=3x^{2}-mx-3x$$

Add m to both sides.

$$nx^{2}-1=3x^{2}-mx-3x+m$$

Add 1 to both sides.

$$nx^{2}=3x^{2}-mx-3x+m+1$$

The equation is in standard form.

$$x^{2}n=3x^{2}-mx-3x+m+1$$

Divide both sides by x^{2}.

$$\frac{x^{2}n}{x^{2}}=\frac{3x^{2}-mx-3x+m+1}{x^{2}}$$

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

$$n=\frac{3x^{2}-mx-3x+m+1}{x^{2}}$$