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Simplifying 7z2 + 27z + -40 = 0 Reorder the terms: -40 + 27z + 7z2 = 0 Solving -40 + 27z + 7z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + -1z)(8 + -7z) = 0Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve: Simplifying -5 + -1z = 0 Solving -5 + -1z = 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 + -1z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z = 0 + 5 -1z = 0 + 5 Combine like terms: 0 + 5 = 5 -1z = 5 Divide each side by '-1'. z = -5 Simplifying z = -5Subproblem 2
Set the factor '(8 + -7z)' equal to zero and attempt to solve: Simplifying 8 + -7z = 0 Solving 8 + -7z = 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 + -7z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7z = 0 + -8 -7z = 0 + -8 Combine like terms: 0 + -8 = -8 -7z = -8 Divide each side by '-7'. z = 1.142857143 Simplifying z = 1.142857143Solution
z = {-5, 1.142857143}
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