4x-2x(1-x)=2(3x-2)

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Solution for 4x-2x(1-x)=2(3x-2) equation:


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

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

Reorder the terms:
2x + 2x2 = 2(-2 + 3x)
2x + 2x2 = (-2 * 2 + 3x * 2)
2x + 2x2 = (-4 + 6x)

Solving
2x + 2x2 = -4 + 6x

Solving for variable 'x'.

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

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

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

Combine like terms: -4 + 4 = 0
4 + -4x + 2x2 = 0 + 6x + -6x
4 + -4x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
4 + -4x + 2x2 = 0

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

Ignore the factor 2.

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

Simplifying
2 + -2x + x2 = 0

Solving
2 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -2x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -2x + x2 = 0 + -2

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

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

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

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

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

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

Factor a perfect square on the left side:
(x + -1)(x + -1) = -1

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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