2x(2x-5)(3x-2)=0

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Solution for 2x(2x-5)(3x-2)=0 equation: 


Simplifying
2x(2x + -5)(3x + -2) = 0

Reorder the terms:
2x(-5 + 2x)(3x + -2) = 0

Reorder the terms:
2x(-5 + 2x)(-2 + 3x) = 0

Multiply (-5 + 2x) * (-2 + 3x)
2x(-5(-2 + 3x) + 2x * (-2 + 3x)) = 0
2x((-2 * -5 + 3x * -5) + 2x * (-2 + 3x)) = 0
2x((10 + -15x) + 2x * (-2 + 3x)) = 0
2x(10 + -15x + (-2 * 2x + 3x * 2x)) = 0
2x(10 + -15x + (-4x + 6x2)) = 0

Combine like terms: -15x + -4x = -19x
2x(10 + -19x + 6x2) = 0
(10 * 2x + -19x * 2x + 6x2 * 2x) = 0
(20x + -38x2 + 12x3) = 0

Solving
20x + -38x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(10 + -19x + 6x2) = 0

Factor a trinomial.
2x((2 + -3x)(5 + -2x)) = 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 '(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 3
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 0.6666666667, 2.5}

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