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Simplifying z3 + -2z2 + -80z = 0 Reorder the terms: -80z + -2z2 + z3 = 0 Solving -80z + -2z2 + z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-80 + -2z + z2) = 0 Factor a trinomial. z((-8 + -1z)(10 + -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 '(-8 + -1z)' equal to zero and attempt to solve: Simplifying -8 + -1z = 0 Solving -8 + -1z = 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 + -1z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1z = 0 + 8 -1z = 0 + 8 Combine like terms: 0 + 8 = 8 -1z = 8 Divide each side by '-1'. z = -8 Simplifying z = -8Subproblem 3
Set the factor '(10 + -1z)' equal to zero and attempt to solve: Simplifying 10 + -1z = 0 Solving 10 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1z = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1z = 0 + -10 -1z = 0 + -10 Combine like terms: 0 + -10 = -10 -1z = -10 Divide each side by '-1'. z = 10 Simplifying z = 10Solution
z = {0, -8, 10}
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