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

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


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

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

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

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

Solving for variable 'x'.

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

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

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

Reorder the terms:
-4 + 4x + -1x2 = 3 + -3 + -3x + 3x + x2 + -1x2

Combine like terms: 3 + -3 = 0
-4 + 4x + -1x2 = 0 + -3x + 3x + x2 + -1x2
-4 + 4x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 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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