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Simplifying z2 + -13z + 24 = -12 Reorder the terms: 24 + -13z + z2 = -12 Solving 24 + -13z + z2 = -12 Solving for variable 'z'. Reorder the terms: 24 + 12 + -13z + z2 = -12 + 12 Combine like terms: 24 + 12 = 36 36 + -13z + z2 = -12 + 12 Combine like terms: -12 + 12 = 0 36 + -13z + z2 = 0 Factor a trinomial. (4 + -1z)(9 + -1z) = 0Subproblem 1
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Subproblem 2
Set the factor '(9 + -1z)' equal to zero and attempt to solve: Simplifying 9 + -1z = 0 Solving 9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1z = 0 + -9 -1z = 0 + -9 Combine like terms: 0 + -9 = -9 -1z = -9 Divide each side by '-1'. z = 9 Simplifying z = 9Solution
z = {4, 9}
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