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Simplifying -32z2 + 4z + 15 = 0 Reorder the terms: 15 + 4z + -32z2 = 0 Solving 15 + 4z + -32z2 = 0 Solving for variable 'z'. Factor a trinomial. (3 + -4z)(5 + 8z) = 0Subproblem 1
Set the factor '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Subproblem 2
Set the factor '(5 + 8z)' equal to zero and attempt to solve: Simplifying 5 + 8z = 0 Solving 5 + 8z = 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 + 8z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8z = 0 + -5 8z = 0 + -5 Combine like terms: 0 + -5 = -5 8z = -5 Divide each side by '8'. z = -0.625 Simplifying z = -0.625Solution
z = {0.75, -0.625}
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