2x-3=1-2x+x^2

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Solution for 2x-3=1-2x+x^2 equation: 


Simplifying
2x + -3 = 1 + -2x + x2

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

Solving
-3 + 2x = 1 + -2x + x2

Solving for variable 'x'.

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

Combine like terms: -3 + -1 = -4
-4 + 2x + 2x + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: 2x + 2x = 4x
-4 + 4x + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Reorder the terms:
-4 + 4x + -1x2 = 1 + -1 + -2x + 2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
-4 + 4x + -1x2 = 0 + -2x + 2x + x2 + -1x2
-4 + 4x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-4 + 4x + -1x2 = 0 + x2 + -1x2
-4 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 4x + -1x2 = 0

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


Subproblem 1
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

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 = {2, 2}

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