Whakaoti i te 2(m+1)x=3(m+1)(m-2)

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

Whakaoti mō x (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te m+1.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2m+2 ki te x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te m+1.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 3m+3 ki te m-2 ka whakakotahi i ngā kupu rite.

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

Pahekotia ngā kīanga tau katoa e whai ana i te x.

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

Whakawehea ngā taha e rua ki te 2m+2.

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

Mā te whakawehe ki te 2m+2 ka wetekia te whakareanga ki te 2m+2.

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

Whakawehe 3\left(-2+m\right)\left(1+m\right) ki te 2m+2.

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

Whakaoti mō x

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te m+1.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2m+2 ki te x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te m+1.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 3m+3 ki te m-2 ka whakakotahi i ngā kupu rite.

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

Pahekotia ngā kīanga tau katoa e whai ana i te x.

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

Whakawehea ngā taha e rua ki te 2m+2.

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

Mā te whakawehe ki te 2m+2 ka wetekia te whakareanga ki te 2m+2.

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

Whakawehe 3\left(-2+m\right)\left(1+m\right) ki te 2m+2.

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

Whakaoti mō m

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

$$m=-1$$