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Simplifying -18z3 + 14z2 + 4z = 0 Reorder the terms: 4z + 14z2 + -18z3 = 0 Solving 4z + 14z2 + -18z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(2 + 7z + -9z2) = 0 Factor a trinomial. 2z((1 + -1z)(2 + 9z)) = 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 '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Subproblem 3
Set the factor '(2 + 9z)' equal to zero and attempt to solve: Simplifying 2 + 9z = 0 Solving 2 + 9z = 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 + 9z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9z = 0 + -2 9z = 0 + -2 Combine like terms: 0 + -2 = -2 9z = -2 Divide each side by '9'. z = -0.2222222222 Simplifying z = -0.2222222222Solution
z = {0, 1, -0.2222222222}
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