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Simplifying 6z2 + 5 + 17z = 0 Reorder the terms: 5 + 17z + 6z2 = 0 Solving 5 + 17z + 6z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + 2z)(1 + 3z) = 0Subproblem 1
Set the factor '(5 + 2z)' equal to zero and attempt to solve: Simplifying 5 + 2z = 0 Solving 5 + 2z = 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 + 2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2z = 0 + -5 2z = 0 + -5 Combine like terms: 0 + -5 = -5 2z = -5 Divide each side by '2'. z = -2.5 Simplifying z = -2.5Subproblem 2
Set the factor '(1 + 3z)' equal to zero and attempt to solve: Simplifying 1 + 3z = 0 Solving 1 + 3z = 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 + 3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3z = 0 + -1 3z = 0 + -1 Combine like terms: 0 + -1 = -1 3z = -1 Divide each side by '3'. z = -0.3333333333 Simplifying z = -0.3333333333Solution
z = {-2.5, -0.3333333333}
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