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Simplifying -4z = -6z3 + -5z2 Reorder the terms: -4z = -5z2 + -6z3 Solving -4z = -5z2 + -6z3 Solving for variable 'z'. Reorder the terms: -4z + 5z2 + 6z3 = -5z2 + 5z2 + -6z3 + 6z3 Combine like terms: -5z2 + 5z2 = 0 -4z + 5z2 + 6z3 = 0 + -6z3 + 6z3 -4z + 5z2 + 6z3 = -6z3 + 6z3 Combine like terms: -6z3 + 6z3 = 0 -4z + 5z2 + 6z3 = 0 Factor out the Greatest Common Factor (GCF), 'z'. z(-4 + 5z + 6z2) = 0 Factor a trinomial. z((-4 + -3z)(1 + -2z)) = 0Subproblem 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 '(-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 = -1.333333333Subproblem 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, -1.333333333, 0.5}
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