(3x-12)(6x-2)=0

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Solution for (3x-12)(6x-2)=0 equation: 


Simplifying
(3x + -12)(6x + -2) = 0

Reorder the terms:
(-12 + 3x)(6x + -2) = 0

Reorder the terms:
(-12 + 3x)(-2 + 6x) = 0

Multiply (-12 + 3x) * (-2 + 6x)
(-12(-2 + 6x) + 3x * (-2 + 6x)) = 0
((-2 * -12 + 6x * -12) + 3x * (-2 + 6x)) = 0
((24 + -72x) + 3x * (-2 + 6x)) = 0
(24 + -72x + (-2 * 3x + 6x * 3x)) = 0
(24 + -72x + (-6x + 18x2)) = 0

Combine like terms: -72x + -6x = -78x
(24 + -78x + 18x2) = 0

Solving
24 + -78x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + -13x + 3x2) = 0

Factor a trinomial.
6((1 + -3x)(4 + -1x)) = 0

Ignore the factor 6.

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.3333333333, 4}

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