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Simplifying -2y(y4 + -2y2 + 1) = 0 Reorder the terms: -2y(1 + -2y2 + y4) = 0 (1 * -2y + -2y2 * -2y + y4 * -2y) = 0 (-2y + 4y3 + -2y5) = 0 Solving -2y + 4y3 + -2y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(-1 + 2y2 + -1y4) = 0 Factor a trinomial. 2y((-1 + y2)(1 + -1y2)) = 0 Factor a difference between two squares. 2y(((1 + y)(-1 + y))(1 + -1y2)) = 0 Factor a difference between two squares. 2y(((1 + y)(1 + -1y))(1 + y)(-1 + 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 = 0Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1Subproblem 3
Set the factor '(-1 + y)' equal to zero and attempt to solve: Simplifying -1 + y = 0 Solving -1 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + y = 0 + 1 y = 0 + 1 Combine like terms: 0 + 1 = 1 y = 1 Simplifying y = 1Subproblem 4
Set the factor '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1Subproblem 5
Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Solution
y = {0, -1, 1, -1, 1}
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