2(1-y^2)+y+1=0

Solution for 2(1-y^2)+y+1=0 equation:

Simplifying
2(1 + -1y2) + y + 1 = 0
(1 * 2 + -1y2 * 2) + y + 1 = 0
(2 + -2y2) + y + 1 = 0

Reorder the terms:
2 + 1 + y + -2y2 = 0

Combine like terms: 2 + 1 = 3
3 + y + -2y2 = 0

Solving
3 + y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + -2y)(1 + y) = 0

Subproblem 1
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

Simplifying
y = -1
Solution
y = {1.5, -1}