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Simplifying z3 = 18z + -7z2 Solving z3 = 18z + -7z2 Solving for variable 'z'. Reorder the terms: -18z + 7z2 + z3 = 18z + -7z2 + -18z + 7z2 Reorder the terms: -18z + 7z2 + z3 = 18z + -18z + -7z2 + 7z2 Combine like terms: 18z + -18z = 0 -18z + 7z2 + z3 = 0 + -7z2 + 7z2 -18z + 7z2 + z3 = -7z2 + 7z2 Combine like terms: -7z2 + 7z2 = 0 -18z + 7z2 + z3 = 0 Factor out the Greatest Common Factor (GCF), 'z'. z(-18 + 7z + z2) = 0 Factor a trinomial. z((-9 + -1z)(2 + -1z)) = 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 '(-9 + -1z)' equal to zero and attempt to solve: Simplifying -9 + -1z = 0 Solving -9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1z = 0 + 9 -1z = 0 + 9 Combine like terms: 0 + 9 = 9 -1z = 9 Divide each side by '-1'. z = -9 Simplifying z = -9Subproblem 3
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 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 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Solution
z = {0, -9, 2}
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