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Simplifying 16z2 + 30z + -54 = 0 Reorder the terms: -54 + 30z + 16z2 = 0 Solving -54 + 30z + 16z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 15z + 8z2) = 0 Factor a trinomial. 2((-3 + -1z)(9 + -8z)) = 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 '(9 + -8z)' equal to zero and attempt to solve: Simplifying 9 + -8z = 0 Solving 9 + -8z = 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 + -8z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8z = 0 + -9 -8z = 0 + -9 Combine like terms: 0 + -9 = -9 -8z = -9 Divide each side by '-8'. z = 1.125 Simplifying z = 1.125Solution
z = {-3, 1.125}
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