Whakaoti i te (x+1)(x-2)-(4x-1)(3x+5)-6=8x-11(x-3)(x+7)

$$( x + 1 ) ( x - 2 ) - ( 4 x - 1 ) ( 3 x + 5 ) - 6 = 8 x - 11 ( x - 3 ) ( x + 7 )$$

Whakaoti mō x

$$x=13$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$x^{2}-x-2-\left(4x-1\right)\left(3x+5\right)-6=8x-11\left(x-3\right)\left(x+7\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x-1 ki te 3x+5 ka whakakotahi i ngā kupu rite.

$$x^{2}-x-2-\left(12x^{2}+17x-5\right)-6=8x-11\left(x-3\right)\left(x+7\right)$$

Hei kimi i te tauaro o 12x^{2}+17x-5, kimihia te tauaro o ia taurangi.

$$x^{2}-x-2-12x^{2}-17x+5-6=8x-11\left(x-3\right)\left(x+7\right)$$

Pahekotia te x^{2} me -12x^{2}, ka -11x^{2}.

$$-11x^{2}-x-2-17x+5-6=8x-11\left(x-3\right)\left(x+7\right)$$

Pahekotia te -x me -17x, ka -18x.

$$-11x^{2}-18x-2+5-6=8x-11\left(x-3\right)\left(x+7\right)$$

Tāpirihia te -2 ki te 5, ka 3.

$$-11x^{2}-18x+3-6=8x-11\left(x-3\right)\left(x+7\right)$$

Tangohia te 6 i te 3, ka -3.

$$-11x^{2}-18x-3=8x-11\left(x-3\right)\left(x+7\right)$$

Me tāpiri te 11\left(x-3\right)\left(x+7\right) ki ngā taha e rua.

$$-11x^{2}-18x-3+11\left(x-3\right)\left(x+7\right)=8x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 11 ki te x-3.

$$-11x^{2}-18x-3+\left(11x-33\right)\left(x+7\right)=8x$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 11x-33 ki te x+7 ka whakakotahi i ngā kupu rite.

$$-11x^{2}-18x-3+11x^{2}+44x-231=8x$$

Pahekotia te -11x^{2} me 11x^{2}, ka 0.

$$-18x-3+44x-231=8x$$

Pahekotia te -18x me 44x, ka 26x.

$$26x-3-231=8x$$

Tangohia te 231 i te -3, ka -234.

$$26x-234=8x$$

Tangohia te 8x mai i ngā taha e rua.

$$26x-234-8x=0$$

Pahekotia te 26x me -8x, ka 18x.

$$18x-234=0$$

Me tāpiri te 234 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$18x=234$$

Whakawehea ngā taha e rua ki te 18.

$$x=\frac{234}{18}$$

Whakawehea te 234 ki te 18, kia riro ko 13.

$$x=13$$