(4x-12)(3x-2)=0

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Solution for (4x-12)(3x-2)=0 equation: 


Simplifying
(4x + -12)(3x + -2) = 0

Reorder the terms:
(-12 + 4x)(3x + -2) = 0

Reorder the terms:
(-12 + 4x)(-2 + 3x) = 0

Multiply (-12 + 4x) * (-2 + 3x)
(-12(-2 + 3x) + 4x * (-2 + 3x)) = 0
((-2 * -12 + 3x * -12) + 4x * (-2 + 3x)) = 0
((24 + -36x) + 4x * (-2 + 3x)) = 0
(24 + -36x + (-2 * 4x + 3x * 4x)) = 0
(24 + -36x + (-8x + 12x2)) = 0

Combine like terms: -36x + -8x = -44x
(24 + -44x + 12x2) = 0

Solving
24 + -44x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -11x + 3x2) = 0

Factor a trinomial.
4((2 + -3x)(3 + -1x)) = 0

Ignore the factor 4.

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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