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

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

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

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

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

Add '-1' to each side of the equation.
1 + -1x + -1 + 2x2 = 1 + -1 + x

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

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

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

Solving
-1x + 2x2 = x

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1 + x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}