Solve 2(m+1)x=3(m+1)(m-2)

$$2 ( m + 1 ) x = 3 ( m + 1 ) ( m - 2 )$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{3\left(m-2\right)}{2}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&m=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by m+1.

$$\left(2m+2\right)x=3\left(m+1\right)\left(m-2\right)$$

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

$$2mx+2x=3\left(m+1\right)\left(m-2\right)$$

Use the distributive property to multiply 3 by m+1.

$$2mx+2x=\left(3m+3\right)\left(m-2\right)$$

Use the distributive property to multiply 3m+3 by m-2 and combine like terms.

$$2mx+2x=3m^{2}-3m-6$$

Combine all terms containing x.

$$\left(2m+2\right)x=3m^{2}-3m-6$$

Divide both sides by 2m+2.

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

Dividing by 2m+2 undoes the multiplication by 2m+2.

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

Divide 3\left(-2+m\right)\left(1+m\right) by 2m+2.

$$x=\frac{3m}{2}-3$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{3\left(m-2\right)}{2}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&m=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by m+1.

$$\left(2m+2\right)x=3\left(m+1\right)\left(m-2\right)$$

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

$$2mx+2x=3\left(m+1\right)\left(m-2\right)$$

Use the distributive property to multiply 3 by m+1.

$$2mx+2x=\left(3m+3\right)\left(m-2\right)$$

Use the distributive property to multiply 3m+3 by m-2 and combine like terms.

$$2mx+2x=3m^{2}-3m-6$$

Combine all terms containing x.

$$\left(2m+2\right)x=3m^{2}-3m-6$$

Divide both sides by 2m+2.

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

Dividing by 2m+2 undoes the multiplication by 2m+2.

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

Divide 3\left(-2+m\right)\left(1+m\right) by 2m+2.

$$x=\frac{3m}{2}-3$$

Solve for m

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

$$m=-1$$