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Simplifying 64z6 + -32z4 + -60z2 = 0 Reorder the terms: -60z2 + -32z4 + 64z6 = 0 Solving -60z2 + -32z4 + 64z6 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4z2'. 4z2(-15 + -8z2 + 16z4) = 0 Factor a trinomial. 4z2((-3 + -4z2)(5 + -4z2)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z2 = 0 Take the square root of each side: z = {0}Subproblem 2
Set the factor '(-3 + -4z2)' equal to zero and attempt to solve: Simplifying -3 + -4z2 = 0 Solving -3 + -4z2 = 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 + -4z2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4z2 = 0 + 3 -4z2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4z2 = 3 Divide each side by '-4'. z2 = -0.75 Simplifying z2 = -0.75 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 '(5 + -4z2)' equal to zero and attempt to solve: Simplifying 5 + -4z2 = 0 Solving 5 + -4z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4z2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4z2 = 0 + -5 -4z2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4z2 = -5 Divide each side by '-4'. z2 = 1.25 Simplifying z2 = 1.25 Take the square root of each side: z = {-1.118033989, 1.118033989}Solution
z = {0, -1.118033989, 1.118033989}
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