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

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


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

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

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

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

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

Reorder the terms for easier multiplication:
2 * -2x = 2x2 + -3x + 1

Multiply 2 * -2
-4x = 2x2 + -3x + 1

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + x + 2x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1 + x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + x + 2x2 = 0

Solving
1 + x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.5x + x2 = 0 + -0.5
0.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.5x + x2 = -0.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5x + 0.25 + x2 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.5x + x2 = -0.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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