8t^3-32t=0

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Solution for 8t^3-32t=0 equation:


Simplifying
8t3 + -32t = 0

Reorder the terms:
-32t + 8t3 = 0

Solving
-32t + 8t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8t'.
8t(-4 + t2) = 0

Factor a difference between two squares.
8t((2 + t)(-2 + t)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0

Subproblem 2

Set the factor '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Simplifying t = -2

Subproblem 3

Set the factor '(-2 + t)' equal to zero and attempt to solve: Simplifying -2 + t = 0 Solving -2 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + t = 0 + 2 t = 0 + 2 Combine like terms: 0 + 2 = 2 t = 2 Simplifying t = 2

Solution

t = {0, -2, 2}

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