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Simplifying 6z2 + 13z + -5 = 0 Reorder the terms: -5 + 13z + 6z2 = 0 Solving -5 + 13z + 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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