(6x-4)(2-2x)-2x(2-2x)=0

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Solution for (6x-4)(2-2x)-2x(2-2x)=0 equation: 


Simplifying
(6x + -4)(2 + -2x) + -2x(2 + -2x) = 0

Reorder the terms:
(-4 + 6x)(2 + -2x) + -2x(2 + -2x) = 0

Multiply (-4 + 6x) * (2 + -2x)
(-4(2 + -2x) + 6x * (2 + -2x)) + -2x(2 + -2x) = 0
((2 * -4 + -2x * -4) + 6x * (2 + -2x)) + -2x(2 + -2x) = 0
((-8 + 8x) + 6x * (2 + -2x)) + -2x(2 + -2x) = 0
(-8 + 8x + (2 * 6x + -2x * 6x)) + -2x(2 + -2x) = 0
(-8 + 8x + (12x + -12x2)) + -2x(2 + -2x) = 0

Combine like terms: 8x + 12x = 20x
(-8 + 20x + -12x2) + -2x(2 + -2x) = 0
-8 + 20x + -12x2 + (2 * -2x + -2x * -2x) = 0
-8 + 20x + -12x2 + (-4x + 4x2) = 0

Reorder the terms:
-8 + 20x + -4x + -12x2 + 4x2 = 0

Combine like terms: 20x + -4x = 16x
-8 + 16x + -12x2 + 4x2 = 0

Combine like terms: -12x2 + 4x2 = -8x2
-8 + 16x + -8x2 = 0

Solving
-8 + 16x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + 2x + -1x2) = 0

Factor a trinomial.
8((-1 + x)(1 + -1x)) = 0

Ignore the factor 8.

Subproblem 1
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

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

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

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

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