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Simplifying z2 + -1z = 8z + -8 Reorder the terms: -1z + z2 = 8z + -8 Reorder the terms: -1z + z2 = -8 + 8z Solving -1z + z2 = -8 + 8z Solving for variable 'z'. Reorder the terms: 8 + -1z + -8z + z2 = -8 + 8z + 8 + -8z Combine like terms: -1z + -8z = -9z 8 + -9z + z2 = -8 + 8z + 8 + -8z Reorder the terms: 8 + -9z + z2 = -8 + 8 + 8z + -8z Combine like terms: -8 + 8 = 0 8 + -9z + z2 = 0 + 8z + -8z 8 + -9z + z2 = 8z + -8z Combine like terms: 8z + -8z = 0 8 + -9z + z2 = 0 Factor a trinomial. (1 + -1z)(8 + -1z) = 0Subproblem 1
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 = 1Subproblem 2
Set the factor '(8 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 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 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Divide each side by '-1'. z = 8 Simplifying z = 8Solution
z = {1, 8}
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