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12\left(2x^{2}+3x\right)
Tauwehea te 12.
x\left(2x+3\right)
Whakaarohia te 2x^{2}+3x. Tauwehea te x.
12x\left(2x+3\right)
Me tuhi anō te kīanga whakatauwehe katoa.
24x^{2}+36x=0
Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.
x=\frac{-36±\sqrt{36^{2}}}{2\times 24}
Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.
x=\frac{-36±36}{2\times 24}
Tuhia te pūtakerua o te 36^{2}.
x=\frac{-36±36}{48}
Whakareatia 2 ki te 24.
x=\frac{0}{48}
Nā, me whakaoti te whārite x=\frac{-36±36}{48} ina he tāpiri te ±. Tāpiri -36 ki te 36.
x=0
Whakawehe 0 ki te 48.
x=-\frac{72}{48}
Nā, me whakaoti te whārite x=\frac{-36±36}{48} ina he tango te ±. Tango 36 mai i -36.
x=-\frac{3}{2}
Whakahekea te hautanga \frac{-72}{48} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 24.
24x^{2}+36x=24x\left(x-\left(-\frac{3}{2}\right)\right)
Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te 0 mō te x_{1} me te -\frac{3}{2} mō te x_{2}.
24x^{2}+36x=24x\left(x+\frac{3}{2}\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.
24x^{2}+36x=24x\times \frac{2x+3}{2}
Tāpiri \frac{3}{2} ki te x mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
24x^{2}+36x=12x\left(2x+3\right)
Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 24 me te 2.