(2x-8)(3x-2)=0

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Solution for (2x-8)(3x-2)=0 equation: 


Simplifying
(2x + -8)(3x + -2) = 0

Reorder the terms:
(-8 + 2x)(3x + -2) = 0

Reorder the terms:
(-8 + 2x)(-2 + 3x) = 0

Multiply (-8 + 2x) * (-2 + 3x)
(-8(-2 + 3x) + 2x * (-2 + 3x)) = 0
((-2 * -8 + 3x * -8) + 2x * (-2 + 3x)) = 0
((16 + -24x) + 2x * (-2 + 3x)) = 0
(16 + -24x + (-2 * 2x + 3x * 2x)) = 0
(16 + -24x + (-4x + 6x2)) = 0

Combine like terms: -24x + -4x = -28x
(16 + -28x + 6x2) = 0

Solving
16 + -28x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -14x + 3x2) = 0

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

Ignore the factor 2.

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 '(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 = {0.6666666667, 4}

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