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Simplifying z2 = 4z + 96 Reorder the terms: z2 = 96 + 4z Solving z2 = 96 + 4z Solving for variable 'z'. Reorder the terms: -96 + -4z + z2 = 96 + 4z + -96 + -4z Reorder the terms: -96 + -4z + z2 = 96 + -96 + 4z + -4z Combine like terms: 96 + -96 = 0 -96 + -4z + z2 = 0 + 4z + -4z -96 + -4z + z2 = 4z + -4z Combine like terms: 4z + -4z = 0 -96 + -4z + z2 = 0 Factor a trinomial. (-8 + -1z)(12 + -1z) = 0Subproblem 1
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 = -8Subproblem 2
Set the factor '(12 + -1z)' equal to zero and attempt to solve: Simplifying 12 + -1z = 0 Solving 12 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1z = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1z = 0 + -12 -1z = 0 + -12 Combine like terms: 0 + -12 = -12 -1z = -12 Divide each side by '-1'. z = 12 Simplifying z = 12Solution
z = {-8, 12}
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