(3x-6)(12x-4)=0

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Solution for (3x-6)(12x-4)=0 equation: 


Simplifying
(3x + -6)(12x + -4) = 0

Reorder the terms:
(-6 + 3x)(12x + -4) = 0

Reorder the terms:
(-6 + 3x)(-4 + 12x) = 0

Multiply (-6 + 3x) * (-4 + 12x)
(-6(-4 + 12x) + 3x * (-4 + 12x)) = 0
((-4 * -6 + 12x * -6) + 3x * (-4 + 12x)) = 0
((24 + -72x) + 3x * (-4 + 12x)) = 0
(24 + -72x + (-4 * 3x + 12x * 3x)) = 0
(24 + -72x + (-12x + 36x2)) = 0

Combine like terms: -72x + -12x = -84x
(24 + -84x + 36x2) = 0

Solving
24 + -84x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(2 + -7x + 3x2) = 0

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

Ignore the factor 12.

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 '(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 = {0.3333333333, 2}

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