0=-9x^3+64x

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Solution for 0=-9x^3+64x equation: 


Simplifying
0 = -9x3 + 64x

Reorder the terms:
0 = 64x + -9x3

Solving
0 = 64x + -9x3

Solving for variable 'x'.
Remove the zero:
-64x + 9x3 = 64x + -9x3 + -64x + 9x3

Reorder the terms:
-64x + 9x3 = 64x + -64x + -9x3 + 9x3

Combine like terms: 64x + -64x = 0
-64x + 9x3 = 0 + -9x3 + 9x3
-64x + 9x3 = -9x3 + 9x3

Combine like terms: -9x3 + 9x3 = 0
-64x + 9x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-64 + 9x2) = 0

Factor a difference between two squares.
x((8 + 3x)(-8 + 3x)) = 0


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 '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 3
Set the factor '(-8 + 3x)' equal to zero and attempt to solve:

Simplifying
-8 + 3x = 0

Solving
-8 + 3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + 3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x = 0 + 8
3x = 0 + 8

Combine like terms: 0 + 8 = 8
3x = 8

Divide each side by '3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {0, -2.666666667, 2.666666667}

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