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

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

x uchun yechish

$$x=13$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

4x-1 ga 3x+5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

12x^{2}+17x-5 teskarisini topish uchun har birining teskarisini toping.

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

-11x^{2} ni olish uchun x^{2} va -12x^{2} ni birlashtirish.

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

-18x ni olish uchun -x va -17x ni birlashtirish.

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

3 olish uchun -2 va 5'ni qo'shing.

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

-3 olish uchun 3 dan 6 ni ayirish.

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

11\left(x-3\right)\left(x+7\right) ni ikki tarafga qo’shing.

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

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

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

11x-33 ga x+7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

0 ni olish uchun -11x^{2} va 11x^{2} ni birlashtirish.

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

26x ni olish uchun -18x va 44x ni birlashtirish.

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

-234 olish uchun -3 dan 231 ni ayirish.

$$26x-234=8x$$

Ikkala tarafdan 8x ni ayirish.

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

18x ni olish uchun 26x va -8x ni birlashtirish.

$$18x-234=0$$

234 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$18x=234$$

Ikki tarafini 18 ga bo‘ling.

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

13 ni olish uchun 234 ni 18 ga bo‘ling.

$$x=13$$