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Simplifying (2z + 9)(3 + z) = 0 Reorder the terms: (9 + 2z)(3 + z) = 0 Multiply (9 + 2z) * (3 + z) (9(3 + z) + 2z * (3 + z)) = 0 ((3 * 9 + z * 9) + 2z * (3 + z)) = 0 ((27 + 9z) + 2z * (3 + z)) = 0 (27 + 9z + (3 * 2z + z * 2z)) = 0 (27 + 9z + (6z + 2z2)) = 0 Combine like terms: 9z + 6z = 15z (27 + 15z + 2z2) = 0 Solving 27 + 15z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + 2z)(3 + z) = 0Subproblem 1
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 = -4.5Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve: Simplifying 3 + z = 0 Solving 3 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + z = 0 + -3 z = 0 + -3 Combine like terms: 0 + -3 = -3 z = -3 Simplifying z = -3Solution
z = {-4.5, -3}
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