(3x-2)(x-4)=6x-4

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Solution for (3x-2)(x-4)=6x-4 equation: 


Simplifying
(3x + -2)(x + -4) = 6x + -4

Reorder the terms:
(-2 + 3x)(x + -4) = 6x + -4

Reorder the terms:
(-2 + 3x)(-4 + x) = 6x + -4

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

Combine like terms: -2x + -12x = -14x
(8 + -14x + 3x2) = 6x + -4

Reorder the terms:
8 + -14x + 3x2 = -4 + 6x

Solving
8 + -14x + 3x2 = -4 + 6x

Solving for variable 'x'.

Reorder the terms:
8 + 4 + -14x + -6x + 3x2 = -4 + 6x + 4 + -6x

Combine like terms: 8 + 4 = 12
12 + -14x + -6x + 3x2 = -4 + 6x + 4 + -6x

Combine like terms: -14x + -6x = -20x
12 + -20x + 3x2 = -4 + 6x + 4 + -6x

Reorder the terms:
12 + -20x + 3x2 = -4 + 4 + 6x + -6x

Combine like terms: -4 + 4 = 0
12 + -20x + 3x2 = 0 + 6x + -6x
12 + -20x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
12 + -20x + 3x2 = 0

Factor a trinomial.
(2 + -3x)(6 + -1x) = 0


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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0.6666666667, 6}

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