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Simplifying 16z3 + -1z = 0 Reorder the terms: -1z + 16z3 = 0 Solving -1z + 16z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-1 + 16z2) = 0 Factor a difference between two squares. z((1 + 4z)(-1 + 4z)) = 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 '(1 + 4z)' equal to zero and attempt to solve: Simplifying 1 + 4z = 0 Solving 1 + 4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4z = 0 + -1 4z = 0 + -1 Combine like terms: 0 + -1 = -1 4z = -1 Divide each side by '4'. z = -0.25 Simplifying z = -0.25Subproblem 3
Set the factor '(-1 + 4z)' equal to zero and attempt to solve: Simplifying -1 + 4z = 0 Solving -1 + 4z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 4z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4z = 0 + 1 4z = 0 + 1 Combine like terms: 0 + 1 = 1 4z = 1 Divide each side by '4'. z = 0.25 Simplifying z = 0.25Solution
z = {0, -0.25, 0.25}
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