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Simplifying (4z + 9)(8 + z) = 0 Reorder the terms: (9 + 4z)(8 + z) = 0 Multiply (9 + 4z) * (8 + z) (9(8 + z) + 4z * (8 + z)) = 0 ((8 * 9 + z * 9) + 4z * (8 + z)) = 0 ((72 + 9z) + 4z * (8 + z)) = 0 (72 + 9z + (8 * 4z + z * 4z)) = 0 (72 + 9z + (32z + 4z2)) = 0 Combine like terms: 9z + 32z = 41z (72 + 41z + 4z2) = 0 Solving 72 + 41z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (8 + z)(9 + 4z) = 0Subproblem 1
Set the factor '(8 + z)' equal to zero and attempt to solve: Simplifying 8 + z = 0 Solving 8 + z = 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 + z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + z = 0 + -8 z = 0 + -8 Combine like terms: 0 + -8 = -8 z = -8 Simplifying z = -8Subproblem 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 = {-8, -2.25}
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