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Simplifying (D4 + 5D2 + -36) * y = 0 Reorder the terms: (-36 + 5D2 + D4) * y = 0 Reorder the terms for easier multiplication: y(-36 + 5D2 + D4) = 0 (-36 * y + 5D2 * y + D4 * y) = 0 (-36y + 5yD2 + yD4) = 0 Solving -36y + 5yD2 + yD4 = 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(-36 + 5D2 + D4) = 0 Factor a trinomial. y((-9 + -1D2)(4 + -1D2)) = 0 Factor a difference between two squares. y((-9 + -1D2)((2 + D)(2 + -1D))) = 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 + -1D2)' equal to zero and attempt to solve: Simplifying -9 + -1D2 = 0 Solving -9 + -1D2 = 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 + -1D2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1D2 = 0 + 9 -1D2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1D2 = 9 Add 'D2' to each side of the equation. -1D2 + D2 = 9 + D2 Combine like terms: -1D2 + D2 = 0 0 = 9 + D2 Simplifying 0 = 9 + D2 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 + D)' equal to zero and attempt to solve: Simplifying 2 + D = 0 Solving 2 + D = 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 + D = 0 + -2 Combine like terms: 2 + -2 = 0 0 + D = 0 + -2 D = 0 + -2 Combine like terms: 0 + -2 = -2 D = -2 Add '-1D' to each side of the equation. D + -1D = -2 + -1D Combine like terms: D + -1D = 0 0 = -2 + -1D Simplifying 0 = -2 + -1D 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 '(2 + -1D)' equal to zero and attempt to solve: Simplifying 2 + -1D = 0 Solving 2 + -1D = 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 + -1D = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1D = 0 + -2 -1D = 0 + -2 Combine like terms: 0 + -2 = -2 -1D = -2 Add 'D' to each side of the equation. -1D + D = -2 + D Combine like terms: -1D + D = 0 0 = -2 + D Simplifying 0 = -2 + D 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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