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Simplifying -28z3 + 16z2 + 80z = 0 Reorder the terms: 80z + 16z2 + -28z3 = 0 Solving 80z + 16z2 + -28z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4z'. 4z(20 + 4z + -7z2) = 0 Factor a trinomial. 4z((2 + -1z)(10 + 7z)) = 0 Ignore the factor 4.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 '(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 = 2Subproblem 3
Set the factor '(10 + 7z)' equal to zero and attempt to solve: Simplifying 10 + 7z = 0 Solving 10 + 7z = 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 + 7z = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 7z = 0 + -10 7z = 0 + -10 Combine like terms: 0 + -10 = -10 7z = -10 Divide each side by '7'. z = -1.428571429 Simplifying z = -1.428571429Solution
z = {0, 2, -1.428571429}
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