Whakaoti i te (2a+4b)(c-6d)=4e+2

$$( 2 a + 4 b ) ( c - 6 d ) = 4 e + 2$$

Whakaoti mō a

$$a=-\frac{2bc-12bd-2e-1}{c-6d}$$

$$c\neq 6d$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2a+4b ki te c-6d.

$$2ac-12da+4bc-24db=4e+2$$

Tangohia te 4bc mai i ngā taha e rua.

$$2ac-12da-24db=4e+2-4bc$$

Me tāpiri te 24db ki ngā taha e rua.

$$2ac-12da=4e+2-4bc+24db$$

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

$$\left(2c-12d\right)a=4e+2-4bc+24db$$

He hanga arowhānui tō te whārite.

$$\left(2c-12d\right)a=2+4e+24bd-4bc$$

Whakawehea ngā taha e rua ki te 2c-12d.

$$\frac{\left(2c-12d\right)a}{2c-12d}=\frac{2+4e+24bd-4bc}{2c-12d}$$

Mā te whakawehe ki te 2c-12d ka wetekia te whakareanga ki te 2c-12d.

$$a=\frac{2+4e+24bd-4bc}{2c-12d}$$

Whakawehe 4e+2-4bc+24db ki te 2c-12d.

$$a=\frac{1+2e+12bd-2bc}{c-6d}$$

Whakaoti mō b

$$b=-\frac{ac-6ad-2e-1}{2\left(c-6d\right)}$$

$$c\neq 6d$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2a+4b ki te c-6d.

$$2ac-12da+4bc-24db=4e+2$$

Tangohia te 2ac mai i ngā taha e rua.

$$-12da+4bc-24db=4e+2-2ac$$

Me tāpiri te 12da ki ngā taha e rua.

$$4bc-24db=4e+2-2ac+12da$$

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

$$\left(4c-24d\right)b=4e+2-2ac+12da$$

He hanga arowhānui tō te whārite.

$$\left(4c-24d\right)b=2+4e+12ad-2ac$$

Whakawehea ngā taha e rua ki te 4c-24d.

$$\frac{\left(4c-24d\right)b}{4c-24d}=\frac{2+4e+12ad-2ac}{4c-24d}$$

Mā te whakawehe ki te 4c-24d ka wetekia te whakareanga ki te 4c-24d.

$$b=\frac{2+4e+12ad-2ac}{4c-24d}$$

Whakawehe 4e+2-2ac+12da ki te 4c-24d.

$$b=\frac{1+2e+6ad-ac}{2\left(c-6d\right)}$$