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Simplifying 24z3 + 22z2 + -30z = 0 Reorder the terms: -30z + 22z2 + 24z3 = 0 Solving -30z + 22z2 + 24z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(-15 + 11z + 12z2) = 0 Factor a trinomial. 2z((-5 + -3z)(3 + -4z)) = 0 Ignore the factor 2.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 + -3z)' equal to zero and attempt to solve: Simplifying -5 + -3z = 0 Solving -5 + -3z = 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 + -3z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3z = 0 + 5 -3z = 0 + 5 Combine like terms: 0 + 5 = 5 -3z = 5 Divide each side by '-3'. z = -1.666666667 Simplifying z = -1.666666667Subproblem 3
Set the factor '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 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 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Solution
z = {0, -1.666666667, 0.75}
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