Solve mx^2-(4m+1)x+3m+3=0

$$m x ^ { 2 } - ( 4 m + 1 ) x + 3 m + 3 = 0$$

Solve for m (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply 4m+1 by x.

$$mx^{2}-\left(4mx+x\right)+3m+3=0$$

To find the opposite of 4mx+x, find the opposite of each term.

$$mx^{2}-4mx-x+3m+3=0$$

Add x to both sides. Anything plus zero gives itself.

$$mx^{2}-4mx+3m+3=x$$

Subtract 3 from both sides.

$$mx^{2}-4mx+3m=x-3$$

Combine all terms containing m.

$$\left(x^{2}-4x+3\right)m=x-3$$

Divide both sides by x^{2}-4x+3.

$$\frac{\left(x^{2}-4x+3\right)m}{x^{2}-4x+3}=\frac{x-3}{x^{2}-4x+3}$$

Dividing by x^{2}-4x+3 undoes the multiplication by x^{2}-4x+3.

$$m=\frac{x-3}{x^{2}-4x+3}$$

Divide -3+x by x^{2}-4x+3.

$$m=\frac{1}{x-1}$$

Solve for m

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

Steps for Solving Linear Equation

Use the distributive property to multiply 4m+1 by x.

$$mx^{2}-\left(4mx+x\right)+3m+3=0$$

To find the opposite of 4mx+x, find the opposite of each term.

$$mx^{2}-4mx-x+3m+3=0$$

Add x to both sides. Anything plus zero gives itself.

$$mx^{2}-4mx+3m+3=x$$

Subtract 3 from both sides.

$$mx^{2}-4mx+3m=x-3$$

Combine all terms containing m.

$$\left(x^{2}-4x+3\right)m=x-3$$

Divide both sides by x^{2}-4x+3.

$$\frac{\left(x^{2}-4x+3\right)m}{x^{2}-4x+3}=\frac{x-3}{x^{2}-4x+3}$$

Dividing by x^{2}-4x+3 undoes the multiplication by x^{2}-4x+3.

$$m=\frac{x-3}{x^{2}-4x+3}$$

Divide -3+x by x^{2}-4x+3.

$$m=\frac{1}{x-1}$$

Solve for x

$$\left\{\begin{matrix}\\x=3\text{, }&\text{unconditionally}\\x=1+\frac{1}{m}\text{, }&m\neq 0\end{matrix}\right.$$