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Simplifying 8z3 + 32z2 = 168z Reorder the terms: 32z2 + 8z3 = 168z Solving 32z2 + 8z3 = 168z Solving for variable 'z'. Reorder the terms: -168z + 32z2 + 8z3 = 168z + -168z Combine like terms: 168z + -168z = 0 -168z + 32z2 + 8z3 = 0 Factor out the Greatest Common Factor (GCF), '8z'. 8z(-21 + 4z + z2) = 0 Factor a trinomial. 8z((-7 + -1z)(3 + -1z)) = 0 Ignore the factor 8.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 '(-7 + -1z)' equal to zero and attempt to solve: Simplifying -7 + -1z = 0 Solving -7 + -1z = 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 + -1z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1z = 0 + 7 -1z = 0 + 7 Combine like terms: 0 + 7 = 7 -1z = 7 Divide each side by '-1'. z = -7 Simplifying z = -7Subproblem 3
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 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 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {0, -7, 3}
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