Solve m^2(x-1)+2=m(2x-1)

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

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply m^{2} by x-1.

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

Use the distributive property to multiply m by 2x-1.

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

Subtract 2mx from both sides.

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

Add m^{2} to both sides.

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

Subtract 2 from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by m^{2}-2m.

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

Dividing by m^{2}-2m undoes the multiplication by m^{2}-2m.

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

Divide \left(-2+m\right)\left(1+m\right) by m^{2}-2m.

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

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply m^{2} by x-1.

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

Use the distributive property to multiply m by 2x-1.

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

Subtract 2mx from both sides.

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

Add m^{2} to both sides.

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

Subtract 2 from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by m^{2}-2m.

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

Dividing by m^{2}-2m undoes the multiplication by m^{2}-2m.

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

Divide \left(-2+m\right)\left(1+m\right) by m^{2}-2m.

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

Solve for m

$$\left\{\begin{matrix}\\m=2\text{, }&\text{unconditionally}\\m=\frac{1}{x-1}\text{, }&x\neq 1\end{matrix}\right.$$