Solve m^2x+4=2m(x+2)

$$m ^ { 2 } x + 4 = 2 m ( x + 2 )$$

Solve for x

$$x=-\frac{4\left(1-m\right)}{m\left(m-2\right)}$$

$$m\neq 2\text{ and }m\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2m by x+2.

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

Subtract 2mx from both sides.

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

Subtract 4 from both sides.

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

Combine all terms containing x.

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

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

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

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

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

Divide -4+4m by m^{2}-2m.

$$x=\frac{4\left(m-1\right)}{m\left(m-2\right)}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{\sqrt{x^{2}+4}+x+2}{x}\text{; }m=\frac{-\sqrt{x^{2}+4}+x+2}{x}\text{, }&x\neq 0\\m=1\text{, }&x=0\end{matrix}\right.$$