Solve 6x^3y+8xy^2-2y=2xy(3x^2+4y)

$$6 { x }^{ 3 } y+8x { y }^{ 2 } -2y=2xy(3 { x }^{ 2 } +4y)$$

Solve for y

$$y=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2xy by 3x^{2}+4y.

$$6x^{3}y+8xy^{2}-2y=6x^{3}y+8xy^{2}$$

Subtract 6x^{3}y from both sides.

$$6x^{3}y+8xy^{2}-2y-6x^{3}y=8xy^{2}$$

Combine 6x^{3}y and -6x^{3}y to get 0.

$$8xy^{2}-2y=8xy^{2}$$

Subtract 8xy^{2} from both sides.

$$8xy^{2}-2y-8xy^{2}=0$$

Combine 8xy^{2} and -8xy^{2} to get 0.

$$-2y=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -2 is not equal to 0, y must be equal to 0.

$$y=0$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

$$y=0$$

Solve for x

$$x\in \mathrm{R}$$

$$y=0$$