(3x-2)(2x-6)=0

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Solution for (3x-2)(2x-6)=0 equation: 


Simplifying
(3x + -2)(2x + -6) = 0

Reorder the terms:
(-2 + 3x)(2x + -6) = 0

Reorder the terms:
(-2 + 3x)(-6 + 2x) = 0

Multiply (-2 + 3x) * (-6 + 2x)
(-2(-6 + 2x) + 3x * (-6 + 2x)) = 0
((-6 * -2 + 2x * -2) + 3x * (-6 + 2x)) = 0
((12 + -4x) + 3x * (-6 + 2x)) = 0
(12 + -4x + (-6 * 3x + 2x * 3x)) = 0
(12 + -4x + (-18x + 6x2)) = 0

Combine like terms: -4x + -18x = -22x
(12 + -22x + 6x2) = 0

Solving
12 + -22x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -11x + 3x2) = 0

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

Ignore the factor 2.

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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.6666666667, 3}

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