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Simplifying 2z = -4z3 + -6z2 Reorder the terms: 2z = -6z2 + -4z3 Solving 2z = -6z2 + -4z3 Solving for variable 'z'. Reorder the terms: 2z + 6z2 + 4z3 = -6z2 + 6z2 + -4z3 + 4z3 Combine like terms: -6z2 + 6z2 = 0 2z + 6z2 + 4z3 = 0 + -4z3 + 4z3 2z + 6z2 + 4z3 = -4z3 + 4z3 Combine like terms: -4z3 + 4z3 = 0 2z + 6z2 + 4z3 = 0 Factor out the Greatest Common Factor (GCF), '2z'. 2z(1 + 3z + 2z2) = 0 Factor a trinomial. 2z((1 + z)(1 + 2z)) = 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 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 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 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Subproblem 3
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 = -0.5Solution
z = {0, -1, -0.5}
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