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Simplifying (2z + 9)(2 + -1z) = 0 Reorder the terms: (9 + 2z)(2 + -1z) = 0 Multiply (9 + 2z) * (2 + -1z) (9(2 + -1z) + 2z * (2 + -1z)) = 0 ((2 * 9 + -1z * 9) + 2z * (2 + -1z)) = 0 ((18 + -9z) + 2z * (2 + -1z)) = 0 (18 + -9z + (2 * 2z + -1z * 2z)) = 0 (18 + -9z + (4z + -2z2)) = 0 Combine like terms: -9z + 4z = -5z (18 + -5z + -2z2) = 0 Solving 18 + -5z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -1z)(9 + 2z) = 0Subproblem 1
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Subproblem 2
Set the factor '(9 + 2z)' equal to zero and attempt to solve: Simplifying 9 + 2z = 0 Solving 9 + 2z = 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 + 2z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2z = 0 + -9 2z = 0 + -9 Combine like terms: 0 + -9 = -9 2z = -9 Divide each side by '2'. z = -4.5 Simplifying z = -4.5Solution
z = {2, -4.5}
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