Whakaoti i te 3(2x+1)(2x-1)-4(3x-2)(3x+2)+6x(4x+1)=31

$$3 ( 2 x + 1 ) ( 2 x - 1 ) - 4 ( 3 x - 2 ) ( 3 x + 2 ) + 6 x ( 4 x + 1 ) = 31$$

Whakaoti mō x

$$x=3$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 2x+1.

$$\left(6x+3\right)\left(2x-1\right)-4\left(3x-2\right)\left(3x+2\right)+6x\left(4x+1\right)=31$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 6x+3 ki te 2x-1 ka whakakotahi i ngā kupu rite.

$$12x^{2}-3-4\left(3x-2\right)\left(3x+2\right)+6x\left(4x+1\right)=31$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x ki te 4x+1.

$$12x^{2}-3-4\left(3x-2\right)\left(3x+2\right)+24x^{2}+6x=31$$

Whakamahia te āhuatanga tohatoha hei whakarea te -4 ki te 3x-2.

$$12x^{2}-3+\left(-12x+8\right)\left(3x+2\right)+24x^{2}+6x=31$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -12x+8 ki te 3x+2 ka whakakotahi i ngā kupu rite.

$$12x^{2}-3-36x^{2}+16+24x^{2}+6x=31$$

Pahekotia te 12x^{2} me -36x^{2}, ka -24x^{2}.

$$-24x^{2}-3+16+24x^{2}+6x=31$$

Tāpirihia te -3 ki te 16, ka 13.

$$-24x^{2}+13+24x^{2}+6x=31$$

Pahekotia te -24x^{2} me 24x^{2}, ka 0.

$$13+6x=31$$

Tangohia te 13 mai i ngā taha e rua.

$$6x=31-13$$

Tangohia te 13 i te 31, ka 18.

$$6x=18$$

Whakawehea ngā taha e rua ki te 6.

$$x=\frac{18}{6}$$

Whakawehea te 18 ki te 6, kia riro ko 3.

$$x=3$$