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

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


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

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

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

Multiply (-1 + 3x) * (-2 + 2x)
(-1(-2 + 2x) + 3x * (-2 + 2x)) = 2
((-2 * -1 + 2x * -1) + 3x * (-2 + 2x)) = 2
((2 + -2x) + 3x * (-2 + 2x)) = 2
(2 + -2x + (-2 * 3x + 2x * 3x)) = 2
(2 + -2x + (-6x + 6x2)) = 2

Combine like terms: -2x + -6x = -8x
(2 + -8x + 6x2) = 2

Add '-2' to each side of the equation.
2 + -8x + -2 + 6x2 = 2 + -2

Reorder the terms:
2 + -2 + -8x + 6x2 = 2 + -2

Combine like terms: 2 + -2 = 0
0 + -8x + 6x2 = 2 + -2
-8x + 6x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-8x + 6x2 = 0

Solving
-8x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-4 + 3x) = 0

Ignore the factor 2.

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 '(-4 + 3x)' equal to zero and attempt to solve:

Simplifying
-4 + 3x = 0

Solving
-4 + 3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + 3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3x = 0 + 4
3x = 0 + 4

Combine like terms: 0 + 4 = 4
3x = 4

Divide each side by '3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, 1.333333333}

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