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

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


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

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

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

Multiply (-4 + 6x) * (-6 + 6x)
(-4(-6 + 6x) + 6x * (-6 + 6x)) = 0
((-6 * -4 + 6x * -4) + 6x * (-6 + 6x)) = 0
((24 + -24x) + 6x * (-6 + 6x)) = 0
(24 + -24x + (-6 * 6x + 6x * 6x)) = 0
(24 + -24x + (-36x + 36x2)) = 0

Combine like terms: -24x + -36x = -60x
(24 + -60x + 36x2) = 0

Solving
24 + -60x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(2 + -5x + 3x2) = 0

Factor a trinomial.
12((2 + -3x)(1 + -1x)) = 0

Ignore the factor 12.

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

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 = {0.6666666667, 1}

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