2y^2+y=1+y+y^2

Solution for 2y^2+y=1+y+y^2 equation:

Simplifying
2y2 + y = 1 + y + y2

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

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

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

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

Solving
2y2 = 1 + y2

Solving for variable 'y'.

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

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

Combine like terms: 2y2 + -1y2 = 1y2
1y2 = 1 + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
1y2 = 1 + 0
1y2 = 1

Divide each side by '1'.
y2 = 1

Simplifying
y2 = 1

Take the square root of each side:
y = {-1, 1}