x^2+y-2y^2=

Solution for x^2+y-2y^2= equation:

Simplifying
x2 + y + -2y2 = 0

Solving
x2 + y + -2y2 = 0

Solving for variable 'x'.

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

Add '-1y' to each side of the equation.
x2 + y + -1y + -2y2 = 0 + -1y

Combine like terms: y + -1y = 0
x2 + 0 + -2y2 = 0 + -1y
x2 + -2y2 = 0 + -1y
Remove the zero:
x2 + -2y2 = -1y

Add '2y2' to each side of the equation.
x2 + -2y2 + 2y2 = -1y + 2y2

Combine like terms: -2y2 + 2y2 = 0
x2 + 0 = -1y + 2y2
x2 = -1y + 2y2

Simplifying
x2 = -1y + 2y2

Reorder the terms:
x2 + y + -2y2 = -1y + y + 2y2 + -2y2

Combine like terms: -1y + y = 0
x2 + y + -2y2 = 0 + 2y2 + -2y2
x2 + y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
x2 + y + -2y2 = 0

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

Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

Combine like terms: -1y + y = 0
x + 0 = 0 + y
x = 0 + y
Remove the zero:
x = y

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

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

Add '-2y' to each side of the equation.
x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
x + 0 = 0 + -2y
x = 0 + -2y
Remove the zero:
x = -2y

Simplifying
x = -2y
Solution
x = {y, -2y}