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

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


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

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

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

Multiply (3 + x) * (-2 + 3x)
2x(3(-2 + 3x) + x(-2 + 3x)) = 0
2x((-2 * 3 + 3x * 3) + x(-2 + 3x)) = 0
2x((-6 + 9x) + x(-2 + 3x)) = 0
2x(-6 + 9x + (-2 * x + 3x * x)) = 0
2x(-6 + 9x + (-2x + 3x2)) = 0

Combine like terms: 9x + -2x = 7x
2x(-6 + 7x + 3x2) = 0
(-6 * 2x + 7x * 2x + 3x2 * 2x) = 0
(-12x + 14x2 + 6x3) = 0

Solving
-12x + 14x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-6 + 7x + 3x2) = 0

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

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, -3, 0.6666666667}

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