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

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


Simplifying
2x(x + -1) + 4 = 2(x + -1)

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
3 + -2x + x2 = 0

Solving
3 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -2x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -2x + x2 = 0 + -3

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

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

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 = -3 + 1

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

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

Factor a perfect square on the left side:
(x + -1)(x + -1) = -2

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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