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Simplifying (16D4 + -40D2 + 9) * y = 0 Reorder the terms: (9 + -40D2 + 16D4) * y = 0 Reorder the terms for easier multiplication: y(9 + -40D2 + 16D4) = 0 (9 * y + -40D2 * y + 16D4 * y) = 0 (9y + -40yD2 + 16yD4) = 0 Solving 9y + -40yD2 + 16yD4 = 0 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'y'. y(9 + -40D2 + 16D4) = 0 Factor a trinomial. y((1 + -4D2)(9 + -4D2)) = 0 Factor a difference between two squares. y(((1 + 2D)(1 + -2D))(9 + -4D2)) = 0 Factor a difference between two squares. y(((3 + 2D)(3 + -2D))(1 + 2D)(1 + -2D)) = 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 '(1 + 2D)' equal to zero and attempt to solve: Simplifying 1 + 2D = 0 Solving 1 + 2D = 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 + 2D = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2D = 0 + -1 2D = 0 + -1 Combine like terms: 0 + -1 = -1 2D = -1 Add '-2D' to each side of the equation. 2D + -2D = -1 + -2D Combine like terms: 2D + -2D = 0 0 = -1 + -2D Simplifying 0 = -1 + -2D 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 '(1 + -2D)' equal to zero and attempt to solve: Simplifying 1 + -2D = 0 Solving 1 + -2D = 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 + -2D = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2D = 0 + -1 -2D = 0 + -1 Combine like terms: 0 + -1 = -1 -2D = -1 Add '2D' to each side of the equation. -2D + 2D = -1 + 2D Combine like terms: -2D + 2D = 0 0 = -1 + 2D Simplifying 0 = -1 + 2D The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(3 + 2D)' equal to zero and attempt to solve: Simplifying 3 + 2D = 0 Solving 3 + 2D = 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 + 2D = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2D = 0 + -3 2D = 0 + -3 Combine like terms: 0 + -3 = -3 2D = -3 Add '-2D' to each side of the equation. 2D + -2D = -3 + -2D Combine like terms: 2D + -2D = 0 0 = -3 + -2D Simplifying 0 = -3 + -2D The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 5
Set the factor '(3 + -2D)' equal to zero and attempt to solve: Simplifying 3 + -2D = 0 Solving 3 + -2D = 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 + -2D = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2D = 0 + -3 -2D = 0 + -3 Combine like terms: 0 + -3 = -3 -2D = -3 Add '2D' to each side of the equation. -2D + 2D = -3 + 2D Combine like terms: -2D + 2D = 0 0 = -3 + 2D Simplifying 0 = -3 + 2D The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
y = {0}
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