Whakaoti i te -3x(c-x)=6e(2e-c)

$$- 3 x ( c - x ) = 6 e ( 2 e - c )$$

Whakaoti mō c (complex solution)

$$\left\{\begin{matrix}c=x+2e\text{, }&x\neq 2e\\c\in \mathrm{C}\text{, }&x=2e\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te -3x ki te c-x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 6e ki te 2e-c.

$$-3xc+3x^{2}=12e^{2}-6ec$$

Me tāpiri te 6ec ki ngā taha e rua.

$$-3xc+3x^{2}+6ec=12e^{2}$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$-3xc+6ec=12e^{2}-3x^{2}$$

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

$$\left(-3x+6e\right)c=12e^{2}-3x^{2}$$

He hanga arowhānui tō te whārite.

$$\left(6e-3x\right)c=12e^{2}-3x^{2}$$

Whakawehea ngā taha e rua ki te -3x+6e.

$$\frac{\left(6e-3x\right)c}{6e-3x}=\frac{12e^{2}-3x^{2}}{6e-3x}$$

Mā te whakawehe ki te -3x+6e ka wetekia te whakareanga ki te -3x+6e.

$$c=\frac{12e^{2}-3x^{2}}{6e-3x}$$

Whakawehe 12e^{2}-3x^{2} ki te -3x+6e.

$$c=x+2e$$

Whakaoti mō c

$$\left\{\begin{matrix}c=x+2e\text{, }&x\neq 2e\\c\in \mathrm{R}\text{, }&x=2e\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te -3x ki te c-x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 6e ki te 2e-c.

$$-3xc+3x^{2}=12e^{2}-6ec$$

Me tāpiri te 6ec ki ngā taha e rua.

$$-3xc+3x^{2}+6ec=12e^{2}$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$-3xc+6ec=12e^{2}-3x^{2}$$

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

$$\left(-3x+6e\right)c=12e^{2}-3x^{2}$$

He hanga arowhānui tō te whārite.

$$\left(6e-3x\right)c=12e^{2}-3x^{2}$$

Whakawehea ngā taha e rua ki te -3x+6e.

$$\frac{\left(6e-3x\right)c}{6e-3x}=\frac{12e^{2}-3x^{2}}{6e-3x}$$

Mā te whakawehe ki te -3x+6e ka wetekia te whakareanga ki te -3x+6e.

$$c=\frac{12e^{2}-3x^{2}}{6e-3x}$$

Whakawehe 12e^{2}-3x^{2} ki te -3x+6e.

$$c=x+2e$$

Whakaoti mō x (complex solution)

$$x=\frac{-\sqrt{\left(c-4e\right)^{2}}+c}{2}$$

$$x=\frac{\sqrt{\left(c-4e\right)^{2}}+c}{2}$$

Whakaoti mō x

$$x=c-2e$$

$$x=2e$$