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Simplifying 54z2 + -9z = 30 Reorder the terms: -9z + 54z2 = 30 Solving -9z + 54z2 = 30 Solving for variable 'z'. Reorder the terms: -30 + -9z + 54z2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -9z + 54z2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + -3z + 18z2) = 0 Factor a trinomial. 3((-2 + -3z)(5 + -6z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -3z)' equal to zero and attempt to solve: Simplifying -2 + -3z = 0 Solving -2 + -3z = 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 + -3z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3z = 0 + 2 -3z = 0 + 2 Combine like terms: 0 + 2 = 2 -3z = 2 Divide each side by '-3'. z = -0.6666666667 Simplifying z = -0.6666666667Subproblem 2
Set the factor '(5 + -6z)' equal to zero and attempt to solve: Simplifying 5 + -6z = 0 Solving 5 + -6z = 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 + -6z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6z = 0 + -5 -6z = 0 + -5 Combine like terms: 0 + -5 = -5 -6z = -5 Divide each side by '-6'. z = 0.8333333333 Simplifying z = 0.8333333333Solution
z = {-0.6666666667, 0.8333333333}
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