3x(2x-5)(3x+1)=0

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Solution for 3x(2x-5)(3x+1)=0 equation: 


Simplifying
3x(2x + -5)(3x + 1) = 0

Reorder the terms:
3x(-5 + 2x)(3x + 1) = 0

Reorder the terms:
3x(-5 + 2x)(1 + 3x) = 0

Multiply (-5 + 2x) * (1 + 3x)
3x(-5(1 + 3x) + 2x * (1 + 3x)) = 0
3x((1 * -5 + 3x * -5) + 2x * (1 + 3x)) = 0
3x((-5 + -15x) + 2x * (1 + 3x)) = 0
3x(-5 + -15x + (1 * 2x + 3x * 2x)) = 0
3x(-5 + -15x + (2x + 6x2)) = 0

Combine like terms: -15x + 2x = -13x
3x(-5 + -13x + 6x2) = 0
(-5 * 3x + -13x * 3x + 6x2 * 3x) = 0
(-15x + -39x2 + 18x3) = 0

Solving
-15x + -39x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-5 + -13x + 6x2) = 0

Factor a trinomial.
3x((-1 + -3x)(5 + -2x)) = 0

Ignore the factor 3.

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 '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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, -0.3333333333, 2.5}

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