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Simplifying 24z2 + 55z + -24 = 0 Reorder the terms: -24 + 55z + 24z2 = 0 Solving -24 + 55z + 24z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + -3z)(3 + -8z) = 0Subproblem 1
Set the factor '(-8 + -3z)' equal to zero and attempt to solve: Simplifying -8 + -3z = 0 Solving -8 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3z = 0 + 8 -3z = 0 + 8 Combine like terms: 0 + 8 = 8 -3z = 8 Divide each side by '-3'. z = -2.666666667 Simplifying z = -2.666666667Subproblem 2
Set the factor '(3 + -8z)' equal to zero and attempt to solve: Simplifying 3 + -8z = 0 Solving 3 + -8z = 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 + -8z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8z = 0 + -3 -8z = 0 + -3 Combine like terms: 0 + -3 = -3 -8z = -3 Divide each side by '-8'. z = 0.375 Simplifying z = 0.375Solution
z = {-2.666666667, 0.375}
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