2x^2-1=1-x-x^2

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

Simplifying
2x2 + -1 = 1 + -1x + -1x2

Reorder the terms:
-1 + 2x2 = 1 + -1x + -1x2

Solving
-1 + 2x2 = 1 + -1x + -1x2

Solving for variable 'x'.

Reorder the terms:
-1 + -1 + x + 2x2 + x2 = 1 + -1x + -1x2 + -1 + x + x2

Combine like terms: -1 + -1 = -2
-2 + x + 2x2 + x2 = 1 + -1x + -1x2 + -1 + x + x2

Combine like terms: 2x2 + x2 = 3x2
-2 + x + 3x2 = 1 + -1x + -1x2 + -1 + x + x2

Reorder the terms:
-2 + x + 3x2 = 1 + -1 + -1x + x + -1x2 + x2

Combine like terms: 1 + -1 = 0
-2 + x + 3x2 = 0 + -1x + x + -1x2 + x2
-2 + x + 3x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
-2 + x + 3x2 = 0 + -1x2 + x2
-2 + x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-2 + x + 3x2 = 0

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

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

Simplifying
-1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -1

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1, 0.6666666667}