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

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


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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

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