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Simplifying 9z3 + -4z = 0 Reorder the terms: -4z + 9z3 = 0 Solving -4z + 9z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-4 + 9z2) = 0 Factor a difference between two squares. z((2 + 3z)(-2 + 3z)) = 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 '(2 + 3z)' equal to zero and attempt to solve: Simplifying 2 + 3z = 0 Solving 2 + 3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3z = 0 + -2 3z = 0 + -2 Combine like terms: 0 + -2 = -2 3z = -2 Divide each side by '3'. z = -0.6666666667 Simplifying z = -0.6666666667Subproblem 3
Set the factor '(-2 + 3z)' equal to zero and attempt to solve: Simplifying -2 + 3z = 0 Solving -2 + 3z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3z = 0 + 2 3z = 0 + 2 Combine like terms: 0 + 2 = 2 3z = 2 Divide each side by '3'. z = 0.6666666667 Simplifying z = 0.6666666667Solution
z = {0, -0.6666666667, 0.6666666667}
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