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

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


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

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

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

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

Combine like terms: -2x + -2x = -4x
(1 + -4x + 4x2) + -3x(1 + -2x) + 2x = 1
1 + -4x + 4x2 + (1 * -3x + -2x * -3x) + 2x = 1
1 + -4x + 4x2 + (-3x + 6x2) + 2x = 1

Reorder the terms:
1 + -4x + -3x + 2x + 4x2 + 6x2 = 1

Combine like terms: -4x + -3x = -7x
1 + -7x + 2x + 4x2 + 6x2 = 1

Combine like terms: -7x + 2x = -5x
1 + -5x + 4x2 + 6x2 = 1

Combine like terms: 4x2 + 6x2 = 10x2
1 + -5x + 10x2 = 1

Add '-1' to each side of the equation.
1 + -5x + -1 + 10x2 = 1 + -1

Reorder the terms:
1 + -1 + -5x + 10x2 = 1 + -1

Combine like terms: 1 + -1 = 0
0 + -5x + 10x2 = 1 + -1
-5x + 10x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-5x + 10x2 = 0

Solving
-5x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-1 + 2x) = 0

Ignore the factor 5.

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 '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2x = 0 + 1

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

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

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, 0.5}

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