2y^2-1=y^2

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

Simplifying
2y2 + -1 = y2

Reorder the terms:
-1 + 2y2 = y2

Solving
-1 + 2y2 = 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.
-1 + 2y2 + -1y2 = y2 + -1y2

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

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

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

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

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

Divide each side by '1'.
y2 = 1

Simplifying
y2 = 1

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