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Simplifying 5z3 + -405z = 0 Reorder the terms: -405z + 5z3 = 0 Solving -405z + 5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z'. 5z(-81 + z2) = 0 Factor a difference between two squares. 5z((9 + z)(-9 + z)) = 0 Ignore the factor 5.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 '(9 + z)' equal to zero and attempt to solve: Simplifying 9 + z = 0 Solving 9 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + z = 0 + -9 z = 0 + -9 Combine like terms: 0 + -9 = -9 z = -9 Simplifying z = -9Subproblem 3
Set the factor '(-9 + z)' equal to zero and attempt to solve: Simplifying -9 + z = 0 Solving -9 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + z = 0 + 9 z = 0 + 9 Combine like terms: 0 + 9 = 9 z = 9 Simplifying z = 9Solution
z = {0, -9, 9}
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