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Simplifying 0 = 16z3 + -1z Reorder the terms: 0 = -1z + 16z3 Solving 0 = -1z + 16z3 Solving for variable 'z'. Remove the zero: z + -16z3 = -1z + 16z3 + z + -16z3 Reorder the terms: z + -16z3 = -1z + z + 16z3 + -16z3 Combine like terms: -1z + z = 0 z + -16z3 = 0 + 16z3 + -16z3 z + -16z3 = 16z3 + -16z3 Combine like terms: 16z3 + -16z3 = 0 z + -16z3 = 0 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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