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Simplifying 0 = -9z2 + -6z + 15 Reorder the terms: 0 = 15 + -6z + -9z2 Solving 0 = 15 + -6z + -9z2 Solving for variable 'z'. Combine like terms: 0 + -15 = -15 -15 + 6z + 9z2 = 15 + -6z + -9z2 + -15 + 6z + 9z2 Reorder the terms: -15 + 6z + 9z2 = 15 + -15 + -6z + 6z + -9z2 + 9z2 Combine like terms: 15 + -15 = 0 -15 + 6z + 9z2 = 0 + -6z + 6z + -9z2 + 9z2 -15 + 6z + 9z2 = -6z + 6z + -9z2 + 9z2 Combine like terms: -6z + 6z = 0 -15 + 6z + 9z2 = 0 + -9z2 + 9z2 -15 + 6z + 9z2 = -9z2 + 9z2 Combine like terms: -9z2 + 9z2 = 0 -15 + 6z + 9z2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 2z + 3z2) = 0 Factor a trinomial. 3((-5 + -3z)(1 + -1z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -3z)' equal to zero and attempt to solve: Simplifying -5 + -3z = 0 Solving -5 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3z = 0 + 5 -3z = 0 + 5 Combine like terms: 0 + 5 = 5 -3z = 5 Divide each side by '-3'. z = -1.666666667 Simplifying z = -1.666666667Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Solution
z = {-1.666666667, 1}
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