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Simplifying 8z3 + -24z2 + -1232z = 0 Reorder the terms: -1232z + -24z2 + 8z3 = 0 Solving -1232z + -24z2 + 8z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '8z'. 8z(-154 + -3z + z2) = 0 Factor a trinomial. 8z((-11 + -1z)(14 + -1z)) = 0 Ignore the factor 8.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 '(-11 + -1z)' equal to zero and attempt to solve: Simplifying -11 + -1z = 0 Solving -11 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1z = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1z = 0 + 11 -1z = 0 + 11 Combine like terms: 0 + 11 = 11 -1z = 11 Divide each side by '-1'. z = -11 Simplifying z = -11Subproblem 3
Set the factor '(14 + -1z)' equal to zero and attempt to solve: Simplifying 14 + -1z = 0 Solving 14 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1z = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1z = 0 + -14 -1z = 0 + -14 Combine like terms: 0 + -14 = -14 -1z = -14 Divide each side by '-1'. z = 14 Simplifying z = 14Solution
z = {0, -11, 14}
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