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Simplifying 16y5 + -81y = 0 Reorder the terms: -81y + 16y5 = 0 Solving -81y + 16y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-81 + 16y4) = 0 Factor a difference between two squares. y((9 + 4y2)(-9 + 4y2)) = 0 Factor a difference between two squares. y((9 + 4y2)((3 + 2y)(-3 + 2y))) = 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 '(9 + 4y2)' equal to zero and attempt to solve: Simplifying 9 + 4y2 = 0 Solving 9 + 4y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4y2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4y2 = 0 + -9 4y2 = 0 + -9 Combine like terms: 0 + -9 = -9 4y2 = -9 Divide each side by '4'. y2 = -2.25 Simplifying y2 = -2.25 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 '(3 + 2y)' equal to zero and attempt to solve: Simplifying 3 + 2y = 0 Solving 3 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2y = 0 + -3 2y = 0 + -3 Combine like terms: 0 + -3 = -3 2y = -3 Divide each side by '2'. y = -1.5 Simplifying y = -1.5Subproblem 4
Set the factor '(-3 + 2y)' equal to zero and attempt to solve: Simplifying -3 + 2y = 0 Solving -3 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2y = 0 + 3 2y = 0 + 3 Combine like terms: 0 + 3 = 3 2y = 3 Divide each side by '2'. y = 1.5 Simplifying y = 1.5Solution
y = {0, -1.5, 1.5}
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