x^2-4*x+3=-x^2+2x+3

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Solution for x^2-4*x+3=-x^2+2x+3 equation: 


Simplifying
x2 + -4x + 3 = -1x2 + 2x + 3

Reorder the terms:
3 + -4x + x2 = -1x2 + 2x + 3

Reorder the terms:
3 + -4x + x2 = 3 + 2x + -1x2

Add '-3' to each side of the equation.
3 + -4x + -3 + x2 = 3 + 2x + -3 + -1x2

Reorder the terms:
3 + -3 + -4x + x2 = 3 + 2x + -3 + -1x2

Combine like terms: 3 + -3 = 0
0 + -4x + x2 = 3 + 2x + -3 + -1x2
-4x + x2 = 3 + 2x + -3 + -1x2

Reorder the terms:
-4x + x2 = 3 + -3 + 2x + -1x2

Combine like terms: 3 + -3 = 0
-4x + x2 = 0 + 2x + -1x2
-4x + x2 = 2x + -1x2

Solving
-4x + x2 = 2x + -1x2

Solving for variable 'x'.

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

Combine like terms: -4x + -2x = -6x
-6x + x2 + x2 = 2x + -1x2 + -2x + x2

Combine like terms: x2 + x2 = 2x2
-6x + 2x2 = 2x + -1x2 + -2x + x2

Reorder the terms:
-6x + 2x2 = 2x + -2x + -1x2 + x2

Combine like terms: 2x + -2x = 0
-6x + 2x2 = 0 + -1x2 + x2
-6x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3 + 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 '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

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

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Solution
x = {0, 3}

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