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Simplifying 12z3 + -22z2 + -14z = 0 Reorder the terms: -14z + -22z2 + 12z3 = 0 Solving -14z + -22z2 + 12z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(-7 + -11z + 6z2) = 0 Factor a trinomial. 2z((-1 + -2z)(7 + -3z)) = 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 + -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 '(7 + -3z)' equal to zero and attempt to solve: Simplifying 7 + -3z = 0 Solving 7 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3z = 0 + -7 -3z = 0 + -7 Combine like terms: 0 + -7 = -7 -3z = -7 Divide each side by '-3'. z = 2.333333333 Simplifying z = 2.333333333Solution
z = {0, -0.5, 2.333333333}
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