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Simplifying (4 + -1z)(4z + 9) = 0 Reorder the terms: (4 + -1z)(9 + 4z) = 0 Multiply (4 + -1z) * (9 + 4z) (4(9 + 4z) + -1z * (9 + 4z)) = 0 ((9 * 4 + 4z * 4) + -1z * (9 + 4z)) = 0 ((36 + 16z) + -1z * (9 + 4z)) = 0 (36 + 16z + (9 * -1z + 4z * -1z)) = 0 (36 + 16z + (-9z + -4z2)) = 0 Combine like terms: 16z + -9z = 7z (36 + 7z + -4z2) = 0 Solving 36 + 7z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + -1z)(9 + 4z) = 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 + 4z)' equal to zero and attempt to solve: Simplifying 9 + 4z = 0 Solving 9 + 4z = 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 + 4z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4z = 0 + -9 4z = 0 + -9 Combine like terms: 0 + -9 = -9 4z = -9 Divide each side by '4'. z = -2.25 Simplifying z = -2.25Solution
z = {4, -2.25}
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