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Simplifying 60z3 + 54z2 + -6z = 0 Reorder the terms: -6z + 54z2 + 60z3 = 0 Solving -6z + 54z2 + 60z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '6z'. 6z(-1 + 9z + 10z2) = 0 Factor a trinomial. 6z((-1 + -1z)(1 + -10z)) = 0 Ignore the factor 6.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 + -1z)' equal to zero and attempt to solve: Simplifying -1 + -1z = 0 Solving -1 + -1z = 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 + -1z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z = 0 + 1 -1z = 0 + 1 Combine like terms: 0 + 1 = 1 -1z = 1 Divide each side by '-1'. z = -1 Simplifying z = -1Subproblem 3
Set the factor '(1 + -10z)' equal to zero and attempt to solve: Simplifying 1 + -10z = 0 Solving 1 + -10z = 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 + -10z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10z = 0 + -1 -10z = 0 + -1 Combine like terms: 0 + -1 = -1 -10z = -1 Divide each side by '-10'. z = 0.1 Simplifying z = 0.1Solution
z = {0, -1, 0.1}
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