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Simplifying 6z3 + -7z2 + -3z = 0 Reorder the terms: -3z + -7z2 + 6z3 = 0 Solving -3z + -7z2 + 6z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-3 + -7z + 6z2) = 0 Factor a trinomial. z((-1 + -3z)(3 + -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 '(-1 + -3z)' equal to zero and attempt to solve: Simplifying -1 + -3z = 0 Solving -1 + -3z = 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 + -3z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3z = 0 + 1 -3z = 0 + 1 Combine like terms: 0 + 1 = 1 -3z = 1 Divide each side by '-3'. z = -0.3333333333 Simplifying z = -0.3333333333Subproblem 3
Set the factor '(3 + -2z)' equal to zero and attempt to solve: Simplifying 3 + -2z = 0 Solving 3 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2z = 0 + -3 -2z = 0 + -3 Combine like terms: 0 + -3 = -3 -2z = -3 Divide each side by '-2'. z = 1.5 Simplifying z = 1.5Solution
z = {0, -0.3333333333, 1.5}
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