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Simplifying 18z3 = 15z2 + 12z Reorder the terms: 18z3 = 12z + 15z2 Solving 18z3 = 12z + 15z2 Solving for variable 'z'. Reorder the terms: -12z + -15z2 + 18z3 = 12z + 15z2 + -12z + -15z2 Reorder the terms: -12z + -15z2 + 18z3 = 12z + -12z + 15z2 + -15z2 Combine like terms: 12z + -12z = 0 -12z + -15z2 + 18z3 = 0 + 15z2 + -15z2 -12z + -15z2 + 18z3 = 15z2 + -15z2 Combine like terms: 15z2 + -15z2 = 0 -12z + -15z2 + 18z3 = 0 Factor out the Greatest Common Factor (GCF), '3z'. 3z(-4 + -5z + 6z2) = 0 Factor a trinomial. 3z((-1 + -2z)(4 + -3z)) = 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 '(-1 + -2z)' equal to zero and attempt to solve: Simplifying -1 + -2z = 0 Solving -1 + -2z = 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 + -2z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2z = 0 + 1 -2z = 0 + 1 Combine like terms: 0 + 1 = 1 -2z = 1 Divide each side by '-2'. z = -0.5 Simplifying z = -0.5Subproblem 3
Set the factor '(4 + -3z)' equal to zero and attempt to solve: Simplifying 4 + -3z = 0 Solving 4 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3z = 0 + -4 -3z = 0 + -4 Combine like terms: 0 + -4 = -4 -3z = -4 Divide each side by '-3'. z = 1.333333333 Simplifying z = 1.333333333Solution
z = {0, -0.5, 1.333333333}
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