2x^2y-xy-y=0

Solution for 2x^2y-xy-y=0 equation:

Simplifying
2x2y + -1xy + -1y = 0

Reorder the terms:
-1xy + 2x2y + -1y = 0

Solving
-1xy + 2x2y + -1y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1x + 2x2 + -1) = 0

Factor a trinomial.
y((x + -1)(2x + 1)) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(x + -1)' equal to zero and attempt to solve:

Simplifying
x + -1 = 0

Reorder the terms:
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1
Subproblem 3
Set the factor '(2x + 1)' equal to zero and attempt to solve:

Simplifying
2x + 1 = 0

Reorder the terms:
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {1, -0.5}