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

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

x uchun yechish

$$x=3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

3 ga 2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

6x+3 ga 2x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

6x ga 4x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-4 ga 3x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-12x+8 ga 3x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

-24x^{2} ni olish uchun 12x^{2} va -36x^{2} ni birlashtirish.

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

13 olish uchun -3 va 16'ni qo'shing.

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

0 ni olish uchun -24x^{2} va 24x^{2} ni birlashtirish.

$$13+6x=31$$

Ikkala tarafdan 13 ni ayirish.

$$6x=31-13$$

18 olish uchun 31 dan 13 ni ayirish.

$$6x=18$$

Ikki tarafini 6 ga bo‘ling.

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

3 ni olish uchun 18 ni 6 ga bo‘ling.

$$x=3$$