2yx^2-2x=0

Solution for 2yx^2-2x=0 equation:

Simplifying
2yx2 + -2x = 0

Reorder the terms:
-2x + 2x2y = 0

Solving
-2x + 2x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1 + xy) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + xy)' equal to zero and attempt to solve:

Simplifying
-1 + xy = 0

Solving
-1 + xy = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + xy = 0 + 1

Combine like terms: -1 + 1 = 0
0 + xy = 0 + 1
xy = 0 + 1

Combine like terms: 0 + 1 = 1
xy = 1

Divide each side by 'y'.
x = y-1

Simplifying
x = y-1
Solution
x = {0, y-1}