How to Solve for x or y in a Horizontal Tangent Problem?

[brambleberry]

Homework Statement

4x - 2xy = 0
how do i solve for EITHER x or y?

Homework Equations

The Attempt at a Solution

i got y = 2 at first but when i plugged it into the original equation to find x it was impossible to get an answer (the x's canceled out)

 

[rock.freak667]

i got y = 2 at first but when i plugged it into the original equation to find x it was impossible to get an answer (the x's canceled out)

the x doesn't cancel out.

4x-2xy=0
2x(2-y)=0

so 2x=0 or 2-y=0.

Meaning x=0,y=2

 

[brambleberry]

the x doesn't cancel out.

4x-2xy=0
2x(2-y)=0

so 2x=0 or 2-y=0.

Meaning x=0,y=2

the original equation is 2y^3 + 6(x^2)y - 12x^2 + 6y = 1

 

[stickplot]

4x-2xy=0
4x=2xy
4=2y
2=y
4x-2x(2)=0
4x=2x(2)
4x=4x
x=1
4(1)-2(1)(2)
4-4=0
yeah i think that's right but not 100% sure