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

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


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

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

Multiply (-2 + 3x) * (3 + -2x)
5x(-2(3 + -2x) + 3x * (3 + -2x)) = 0
5x((3 * -2 + -2x * -2) + 3x * (3 + -2x)) = 0
5x((-6 + 4x) + 3x * (3 + -2x)) = 0
5x(-6 + 4x + (3 * 3x + -2x * 3x)) = 0
5x(-6 + 4x + (9x + -6x2)) = 0

Combine like terms: 4x + 9x = 13x
5x(-6 + 13x + -6x2) = 0
(-6 * 5x + 13x * 5x + -6x2 * 5x) = 0
(-30x + 65x2 + -30x3) = 0

Solving
-30x + 65x2 + -30x3 = 0

Solving for variable 'x'.

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

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

Ignore the factor 5.

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 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 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 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5

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, 1.5, 0.6666666667}

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