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Simplifying 3z4 + -768z2 = 0 Reorder the terms: -768z2 + 3z4 = 0 Solving -768z2 + 3z4 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3z2'. 3z2(-256 + z2) = 0 Factor a difference between two squares. 3z2((16 + z)(-16 + z)) = 0 Ignore the factor 3.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 '(16 + z)' equal to zero and attempt to solve: Simplifying 16 + z = 0 Solving 16 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + z = 0 + -16 Combine like terms: 16 + -16 = 0 0 + z = 0 + -16 z = 0 + -16 Combine like terms: 0 + -16 = -16 z = -16 Simplifying z = -16Subproblem 3
Set the factor '(-16 + z)' equal to zero and attempt to solve: Simplifying -16 + z = 0 Solving -16 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + z = 0 + 16 Combine like terms: -16 + 16 = 0 0 + z = 0 + 16 z = 0 + 16 Combine like terms: 0 + 16 = 16 z = 16 Simplifying z = 16Solution
z = {0, -16, 16}
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