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Simplifying 36z3 + -9z = 0 Reorder the terms: -9z + 36z3 = 0 Solving -9z + 36z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '9z'. 9z(-1 + 4z2) = 0 Factor a difference between two squares. 9z((1 + 2z)(-1 + 2z)) = 0 Ignore the factor 9.Subproblem 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 + 2z)' equal to zero and attempt to solve: Simplifying 1 + 2z = 0 Solving 1 + 2z = 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 + 2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2z = 0 + -1 2z = 0 + -1 Combine like terms: 0 + -1 = -1 2z = -1 Divide each side by '2'. z = -0.5 Simplifying z = -0.5Subproblem 3
Set the factor '(-1 + 2z)' equal to zero and attempt to solve: Simplifying -1 + 2z = 0 Solving -1 + 2z = 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 + 2z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2z = 0 + 1 2z = 0 + 1 Combine like terms: 0 + 1 = 1 2z = 1 Divide each side by '2'. z = 0.5 Simplifying z = 0.5Solution
z = {0, -0.5, 0.5}
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