(3x-2)(6x)(2x+5)=0

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Solution for (3x-2)(6x)(2x+5)=0 equation: 


Simplifying
(3x + -2)(6x)(2x + 5) = 0

Reorder the terms:
(-2 + 3x)(6x)(2x + 5) = 0

Remove parenthesis around (6x)
(-2 + 3x) * 6x(2x + 5) = 0

Reorder the terms:
(-2 + 3x) * 6x(5 + 2x) = 0

Reorder the terms for easier multiplication:
6x(-2 + 3x)(5 + 2x) = 0

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

Combine like terms: -4x + 15x = 11x
6x(-10 + 11x + 6x2) = 0
(-10 * 6x + 11x * 6x + 6x2 * 6x) = 0
(-60x + 66x2 + 36x3) = 0

Solving
-60x + 66x2 + 36x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-10 + 11x + 6x2) = 0

Factor a trinomial.
6x((-5 + -2x)(2 + -3x)) = 0

Ignore the factor 6.

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 + -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

Subproblem 3
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
Solution
x = {0, -2.5, 0.6666666667}

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