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Simplifying y(y4 + 2y2 + -24) = 0 Reorder the terms: y(-24 + 2y2 + y4) = 0 (-24 * y + 2y2 * y + y4 * y) = 0 (-24y + 2y3 + y5) = 0 Solving -24y + 2y3 + y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-24 + 2y2 + y4) = 0 Factor a trinomial. y((-6 + -1y2)(4 + -1y2)) = 0 Factor a difference between two squares. y((-6 + -1y2)((2 + y)(2 + -1y))) = 0Subproblem 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 '(-6 + -1y2)' equal to zero and attempt to solve: Simplifying -6 + -1y2 = 0 Solving -6 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1y2 = 0 + 6 -1y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1y2 = 6 Divide each side by '-1'. y2 = -6 Simplifying y2 = -6 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.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 = -2Subproblem 4
Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 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 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Solution
y = {0, -2, 2}
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