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Simplifying 2z2 + -30z + -108 = 0 Reorder the terms: -108 + -30z + 2z2 = 0 Solving -108 + -30z + 2z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + -15z + z2) = 0 Factor a trinomial. 2((-3 + -1z)(18 + -1z)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 2
Set the factor '(18 + -1z)' equal to zero and attempt to solve: Simplifying 18 + -1z = 0 Solving 18 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1z = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1z = 0 + -18 -1z = 0 + -18 Combine like terms: 0 + -18 = -18 -1z = -18 Divide each side by '-1'. z = 18 Simplifying z = 18Solution
z = {-3, 18}
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