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Simplifying 18z3 + -3z2 = 15z Reorder the terms: -3z2 + 18z3 = 15z Solving -3z2 + 18z3 = 15z Solving for variable 'z'. Reorder the terms: -15z + -3z2 + 18z3 = 15z + -15z Combine like terms: 15z + -15z = 0 -15z + -3z2 + 18z3 = 0 Factor out the Greatest Common Factor (GCF), '3z'. 3z(-5 + -1z + 6z2) = 0 Factor a trinomial. 3z((-5 + -6z)(1 + -1z)) = 0 Ignore the factor 3.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 '(-5 + -6z)' equal to zero and attempt to solve: Simplifying -5 + -6z = 0 Solving -5 + -6z = 0 Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -6z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6z = 0 + 5 -6z = 0 + 5 Combine like terms: 0 + 5 = 5 -6z = 5 Divide each side by '-6'. z = -0.8333333333 Simplifying z = -0.8333333333Subproblem 3
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 = 1Solution
z = {0, -0.8333333333, 1}
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