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Simplifying -7z = -4z2 + -3 Reorder the terms: -7z = -3 + -4z2 Solving -7z = -3 + -4z2 Solving for variable 'z'. Reorder the terms: 3 + -7z + 4z2 = -3 + -4z2 + 3 + 4z2 Reorder the terms: 3 + -7z + 4z2 = -3 + 3 + -4z2 + 4z2 Combine like terms: -3 + 3 = 0 3 + -7z + 4z2 = 0 + -4z2 + 4z2 3 + -7z + 4z2 = -4z2 + 4z2 Combine like terms: -4z2 + 4z2 = 0 3 + -7z + 4z2 = 0 Factor a trinomial. (3 + -4z)(1 + -1z) = 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 '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 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 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Solution
z = {0.75, 1}
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