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

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


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

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

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

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

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

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

Remove parenthesis around (-2 + 2x)
-2 + -2x + 4x2 = -2 + 2x

Add '2' to each side of the equation.
-2 + -2x + 2 + 4x2 = -2 + 2 + 2x

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

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

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

Solving
-2x + 4x2 = 2x

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-1 + x) = 0

Ignore the factor 4.

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 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1
Solution
x = {0, 1}

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