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

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


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

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

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

Multiply (-3 + x) * (-5 + 3x)
2x(-3(-5 + 3x) + x(-5 + 3x)) = 0
2x((-5 * -3 + 3x * -3) + x(-5 + 3x)) = 0
2x((15 + -9x) + x(-5 + 3x)) = 0
2x(15 + -9x + (-5 * x + 3x * x)) = 0
2x(15 + -9x + (-5x + 3x2)) = 0

Combine like terms: -9x + -5x = -14x
2x(15 + -14x + 3x2) = 0
(15 * 2x + -14x * 2x + 3x2 * 2x) = 0
(30x + -28x2 + 6x3) = 0

Solving
30x + -28x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(15 + -14x + 3x2) = 0

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

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

Subproblem 3
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, 1.666666667, 3}

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