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Simplifying 9z2 + -57z + -120 = 0 Reorder the terms: -120 + -57z + 9z2 = 0 Solving -120 + -57z + 9z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3'. 3(-40 + -19z + 3z2) = 0 Factor a trinomial. 3((-5 + -3z)(8 + -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 '(8 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Divide each side by '-1'. z = 8 Simplifying z = 8Solution
z = {-1.666666667, 8}
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