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Simplifying 35z3 + 16z2 + -12z = 0 Reorder the terms: -12z + 16z2 + 35z3 = 0 Solving -12z + 16z2 + 35z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-12 + 16z + 35z2) = 0 Factor a trinomial. z((-6 + -7z)(2 + -5z)) = 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 '(-6 + -7z)' equal to zero and attempt to solve: Simplifying -6 + -7z = 0 Solving -6 + -7z = 0 Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -7z = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7z = 0 + 6 -7z = 0 + 6 Combine like terms: 0 + 6 = 6 -7z = 6 Divide each side by '-7'. z = -0.8571428571 Simplifying z = -0.8571428571Subproblem 3
Set the factor '(2 + -5z)' equal to zero and attempt to solve: Simplifying 2 + -5z = 0 Solving 2 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5z = 0 + -2 -5z = 0 + -2 Combine like terms: 0 + -2 = -2 -5z = -2 Divide each side by '-5'. z = 0.4 Simplifying z = 0.4Solution
z = {0, -0.8571428571, 0.4}
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