0=4x^3-64x

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Solution for 0=4x^3-64x equation:


Simplifying
0 = 4x3 + -64x

Reorder the terms:
0 = -64x + 4x3

Solving
0 = -64x + 4x3

Solving for variable 'x'.
Remove the zero:
64x + -4x3 = -64x + 4x3 + 64x + -4x3

Reorder the terms:
64x + -4x3 = -64x + 64x + 4x3 + -4x3

Combine like terms: -64x + 64x = 0
64x + -4x3 = 0 + 4x3 + -4x3
64x + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
64x + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(16 + -1x2) = 0

Factor a difference between two squares.
4x((4 + x)(4 + -1x)) = 0

Ignore the factor 4.

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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 3

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {0, -4, 4}

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