(3x-2)(2x-4)=14

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Solution for (3x-2)(2x-4)=14 equation:


Simplifying
(3x + -2)(2x + -4) = 14

Reorder the terms:
(-2 + 3x)(2x + -4) = 14

Reorder the terms:
(-2 + 3x)(-4 + 2x) = 14

Multiply (-2 + 3x) * (-4 + 2x)
(-2(-4 + 2x) + 3x * (-4 + 2x)) = 14
((-4 * -2 + 2x * -2) + 3x * (-4 + 2x)) = 14
((8 + -4x) + 3x * (-4 + 2x)) = 14
(8 + -4x + (-4 * 3x + 2x * 3x)) = 14
(8 + -4x + (-12x + 6x2)) = 14

Combine like terms: -4x + -12x = -16x
(8 + -16x + 6x2) = 14

Solving
8 + -16x + 6x2 = 14

Solving for variable 'x'.

Reorder the terms:
8 + -14 + -16x + 6x2 = 14 + -14

Combine like terms: 8 + -14 = -6
-6 + -16x + 6x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-6 + -16x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -8x + 3x2) = 0

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

Ignore the factor 2.

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 '(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 = {-0.3333333333, 3}

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