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Simplifying 16z3 + -9z = 0 Reorder the terms: -9z + 16z3 = 0 Solving -9z + 16z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-9 + 16z2) = 0 Factor a difference between two squares. z((3 + 4z)(-3 + 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 '(3 + 4z)' equal to zero and attempt to solve: Simplifying 3 + 4z = 0 Solving 3 + 4z = 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 + 4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4z = 0 + -3 4z = 0 + -3 Combine like terms: 0 + -3 = -3 4z = -3 Divide each side by '4'. z = -0.75 Simplifying z = -0.75Subproblem 3
Set the factor '(-3 + 4z)' equal to zero and attempt to solve: Simplifying -3 + 4z = 0 Solving -3 + 4z = 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 + 4z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4z = 0 + 3 4z = 0 + 3 Combine like terms: 0 + 3 = 3 4z = 3 Divide each side by '4'. z = 0.75 Simplifying z = 0.75Solution
z = {0, -0.75, 0.75}
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