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Simplifying 2z5 = 32z Solving 2z5 = 32z Solving for variable 'z'. Reorder the terms: -32z + 2z5 = 32z + -32z Combine like terms: 32z + -32z = 0 -32z + 2z5 = 0 Factor out the Greatest Common Factor (GCF), '2z'. 2z(-16 + z4) = 0 Factor a difference between two squares. 2z((4 + z2)(-4 + z2)) = 0 Factor a difference between two squares. 2z((4 + z2)((2 + z)(-2 + z))) = 0 Ignore the factor 2.Subproblem 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 + z2)' equal to zero and attempt to solve: Simplifying 4 + z2 = 0 Solving 4 + z2 = 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 + z2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z2 = 0 + -4 z2 = 0 + -4 Combine like terms: 0 + -4 = -4 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 '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Subproblem 4
Set the factor '(-2 + z)' equal to zero and attempt to solve: Simplifying -2 + z = 0 Solving -2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + z = 0 + 2 z = 0 + 2 Combine like terms: 0 + 2 = 2 z = 2 Simplifying z = 2Solution
z = {0, -2, 2}
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