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

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

Simplifying
(x2 + -1x + 1) + -1(2x2 + -1) = 0

Reorder the terms:
(1 + -1x + x2) + -1(2x2 + -1) = 0

Remove parenthesis around (1 + -1x + x2)
1 + -1x + x2 + -1(2x2 + -1) = 0

Reorder the terms:
1 + -1x + x2 + -1(-1 + 2x2) = 0
1 + -1x + x2 + (-1 * -1 + 2x2 * -1) = 0
1 + -1x + x2 + (1 + -2x2) = 0

Reorder the terms:
1 + 1 + -1x + x2 + -2x2 = 0

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

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

Solving
2 + -1x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(2 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {1, -2}