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

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


Simplifying
5x2(3x + 2)(3x + -2) = 0

Reorder the terms:
5x2(2 + 3x)(3x + -2) = 0

Reorder the terms:
5x2(2 + 3x)(-2 + 3x) = 0

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

Combine like terms: 6x + -6x = 0
5x2(-4 + 0 + 9x2) = 0
5x2(-4 + 9x2) = 0
(-4 * 5x2 + 9x2 * 5x2) = 0
(-20x2 + 45x4) = 0

Solving
-20x2 + 45x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(-4 + 9x2) = 0

Factor a difference between two squares.
5x2((2 + 3x)(-2 + 3x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
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

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, -0.6666666667, 0.6666666667}

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