6x^2y+4xy=2x^2y(3x+2) eching

$$6 x ^ { 2 } y + 4 x y = 2 x ^ { 2 } y ( 3 x + 2 )$$

y uchun yechish (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=-\frac{2}{3}\text{ or }x=1\text{ or }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2x^{2}y ga 3x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}y+4xy=6x^{3}y+4x^{2}y$$

Ikkala tarafdan 6x^{3}y ni ayirish.

$$6x^{2}y+4xy-6x^{3}y=4x^{2}y$$

Ikkala tarafdan 4x^{2}y ni ayirish.

$$6x^{2}y+4xy-6x^{3}y-4x^{2}y=0$$

2x^{2}y ni olish uchun 6x^{2}y va -4x^{2}y ni birlashtirish.

$$2x^{2}y+4xy-6x^{3}y=0$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2x^{2}+4x-6x^{3}\right)y=0$$

Tenglama standart shaklda.

$$\left(4x+2x^{2}-6x^{3}\right)y=0$$

0 ni 2x^{2}+4x-6x^{3} ga bo'lish.

$$y=0$$

y uchun yechish

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=-\frac{2}{3}\text{ or }x=1\text{ or }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2x^{2}y ga 3x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}y+4xy=6x^{3}y+4x^{2}y$$

Ikkala tarafdan 6x^{3}y ni ayirish.

$$6x^{2}y+4xy-6x^{3}y=4x^{2}y$$

Ikkala tarafdan 4x^{2}y ni ayirish.

$$6x^{2}y+4xy-6x^{3}y-4x^{2}y=0$$

2x^{2}y ni olish uchun 6x^{2}y va -4x^{2}y ni birlashtirish.

$$2x^{2}y+4xy-6x^{3}y=0$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2x^{2}+4x-6x^{3}\right)y=0$$

Tenglama standart shaklda.

$$\left(4x+2x^{2}-6x^{3}\right)y=0$$

0 ni 2x^{2}+4x-6x^{3} ga bo'lish.

$$y=0$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}\\x=1\text{; }x=0\text{; }x=-\frac{2}{3}\approx -0,666666667\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}\\x=1\text{; }x=0\text{; }x=-\frac{2}{3}\approx -0,666666667\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right,$$