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

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


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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

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

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