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Simplifying z5 + -5z3 + -36z = 0 Reorder the terms: -36z + -5z3 + z5 = 0 Solving -36z + -5z3 + z5 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-36 + -5z2 + z4) = 0 Factor a trinomial. z((-4 + -1z2)(9 + -1z2)) = 0 Factor a difference between two squares. z((-4 + -1z2)((3 + z)(3 + -1z))) = 0Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(-4 + -1z2)' equal to zero and attempt to solve: Simplifying -4 + -1z2 = 0 Solving -4 + -1z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1z2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1z2 = 0 + 4 -1z2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1z2 = 4 Divide each side by '-1'. z2 = -4 Simplifying z2 = -4 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 + z)' equal to zero and attempt to solve: Simplifying 3 + z = 0 Solving 3 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + z = 0 + -3 z = 0 + -3 Combine like terms: 0 + -3 = -3 z = -3 Simplifying z = -3Subproblem 4
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {0, -3, 3}
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