2x(4x^2-9)(x^2-9)=0

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Solution for 2x(4x^2-9)(x^2-9)=0 equation: 


Simplifying
2x(4x2 + -9)(x2 + -9) = 0

Reorder the terms:
2x(-9 + 4x2)(x2 + -9) = 0

Reorder the terms:
2x(-9 + 4x2)(-9 + x2) = 0

Multiply (-9 + 4x2) * (-9 + x2)
2x(-9(-9 + x2) + 4x2 * (-9 + x2)) = 0
2x((-9 * -9 + x2 * -9) + 4x2 * (-9 + x2)) = 0
2x((81 + -9x2) + 4x2 * (-9 + x2)) = 0
2x(81 + -9x2 + (-9 * 4x2 + x2 * 4x2)) = 0
2x(81 + -9x2 + (-36x2 + 4x4)) = 0

Combine like terms: -9x2 + -36x2 = -45x2
2x(81 + -45x2 + 4x4) = 0
(81 * 2x + -45x2 * 2x + 4x4 * 2x) = 0
(162x + -90x3 + 8x5) = 0

Solving
162x + -90x3 + 8x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(81 + -45x2 + 4x4) = 0

Factor a trinomial.
2x((9 + -4x2)(9 + -1x2)) = 0

Factor a difference between two squares.
2x(((3 + 2x)(3 + -2x))(9 + -1x2)) = 0

Factor a difference between two squares.
2x(((3 + x)(3 + -1x))(3 + 2x)(3 + -2x)) = 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 + 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 '(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 4
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3

Subproblem 5
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
Solution
x = {0, -1.5, 1.5, -3, 3}

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