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Simplifying 9z3 + 18z2 = 135z Reorder the terms: 18z2 + 9z3 = 135z Solving 18z2 + 9z3 = 135z Solving for variable 'z'. Reorder the terms: -135z + 18z2 + 9z3 = 135z + -135z Combine like terms: 135z + -135z = 0 -135z + 18z2 + 9z3 = 0 Factor out the Greatest Common Factor (GCF), '9z'. 9z(-15 + 2z + z2) = 0 Factor a trinomial. 9z((-5 + -1z)(3 + -1z)) = 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 '(-5 + -1z)' equal to zero and attempt to solve: Simplifying -5 + -1z = 0 Solving -5 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z = 0 + 5 -1z = 0 + 5 Combine like terms: 0 + 5 = 5 -1z = 5 Divide each side by '-1'. z = -5 Simplifying z = -5Subproblem 3
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 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 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {0, -5, 3}
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