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Simplifying z3 + 10z2 + -24z = 0 Reorder the terms: -24z + 10z2 + z3 = 0 Solving -24z + 10z2 + z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-24 + 10z + z2) = 0 Factor a trinomial. z((-12 + -1z)(2 + -1z)) = 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 '(-12 + -1z)' equal to zero and attempt to solve: Simplifying -12 + -1z = 0 Solving -12 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1z = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1z = 0 + 12 -1z = 0 + 12 Combine like terms: 0 + 12 = 12 -1z = 12 Divide each side by '-1'. z = -12 Simplifying z = -12Subproblem 3
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 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 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Solution
z = {0, -12, 2}
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