(3x-6)(9x-2)=0

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Solution for (3x-6)(9x-2)=0 equation: 


Simplifying
(3x + -6)(9x + -2) = 0

Reorder the terms:
(-6 + 3x)(9x + -2) = 0

Reorder the terms:
(-6 + 3x)(-2 + 9x) = 0

Multiply (-6 + 3x) * (-2 + 9x)
(-6(-2 + 9x) + 3x * (-2 + 9x)) = 0
((-2 * -6 + 9x * -6) + 3x * (-2 + 9x)) = 0
((12 + -54x) + 3x * (-2 + 9x)) = 0
(12 + -54x + (-2 * 3x + 9x * 3x)) = 0
(12 + -54x + (-6x + 27x2)) = 0

Combine like terms: -54x + -6x = -60x
(12 + -60x + 27x2) = 0

Solving
12 + -60x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -20x + 9x2) = 0

Factor a trinomial.
3((2 + -9x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -9x)' equal to zero and attempt to solve:

Simplifying
2 + -9x = 0

Solving
2 + -9x = 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 + -9x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9x = 0 + -2
-9x = 0 + -2

Combine like terms: 0 + -2 = -2
-9x = -2

Divide each side by '-9'.
x = 0.2222222222

Simplifying
x = 0.2222222222

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.2222222222, 2}

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