Whakaoti i te p=4(3p(p+q))

$$p = 4 ( 3 p ( p + q ) )$$

Whakaoti mō q

$$\left\{\begin{matrix}\\q=\frac{1}{12}-p\text{, }&\text{unconditionally}\\q\in \mathrm{R}\text{, }&p=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te 4 ki te 3, ka 12.

$$p=12p\left(p+q\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 12p ki te p+q.

$$p=12p^{2}+12pq$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$12p^{2}+12pq=p$$

Tangohia te 12p^{2} mai i ngā taha e rua.

$$12pq=p-12p^{2}$$

Whakawehea ngā taha e rua ki te 12p.

$$\frac{12pq}{12p}=\frac{p\left(1-12p\right)}{12p}$$

Mā te whakawehe ki te 12p ka wetekia te whakareanga ki te 12p.

$$q=\frac{p\left(1-12p\right)}{12p}$$

Whakawehe p\left(1-12p\right) ki te 12p.

$$q=\frac{1}{12}-p$$

Whakaoti mō p

$$p=\frac{1}{12}-q$$

$$p=0$$