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

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


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

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

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

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

Combine like terms: -6x + -4x = -10x
2x(8 + -10x + 3x2) = 0
(8 * 2x + -10x * 2x + 3x2 * 2x) = 0
(16x + -20x2 + 6x3) = 0

Solving
16x + -20x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(8 + -10x + 3x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 3
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, 1.333333333, 2}

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