2y^3=8y

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Solution for 2y^3=8y equation:


Simplifying
2y3 = 8y

Solving
2y3 = 8y

Solving for variable 'y'.

Reorder the terms:
-8y + 2y3 = 8y + -8y

Combine like terms: 8y + -8y = 0
-8y + 2y3 = 0

Factor out the Greatest Common Factor (GCF), '2y'.
2y(-4 + y2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0

Subproblem 2

Set the factor '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2

Subproblem 3

Set the factor '(-2 + y)' equal to zero and attempt to solve: Simplifying -2 + y = 0 Solving -2 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + y = 0 + 2 y = 0 + 2 Combine like terms: 0 + 2 = 2 y = 2 Simplifying y = 2

Solution

y = {0, -2, 2}

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