64x^3=4x

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Solution for 64x^3=4x equation:


Simplifying
64x3 = 4x

Solving
64x3 = 4x

Solving for variable 'x'.

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

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

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

Factor a difference between two squares.
4x((1 + 4x)(-1 + 4x)) = 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 '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25

Subproblem 3

Set the factor '(-1 + 4x)' equal to zero and attempt to solve: Simplifying -1 + 4x = 0 Solving -1 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4x = 0 + 1 4x = 0 + 1 Combine like terms: 0 + 1 = 1 4x = 1 Divide each side by '4'. x = 0.25 Simplifying x = 0.25

Solution

x = {0, -0.25, 0.25}

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