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Simplifying (3z + 8)(9 + z) = 0 Reorder the terms: (8 + 3z)(9 + z) = 0 Multiply (8 + 3z) * (9 + z) (8(9 + z) + 3z * (9 + z)) = 0 ((9 * 8 + z * 8) + 3z * (9 + z)) = 0 ((72 + 8z) + 3z * (9 + z)) = 0 (72 + 8z + (9 * 3z + z * 3z)) = 0 (72 + 8z + (27z + 3z2)) = 0 Combine like terms: 8z + 27z = 35z (72 + 35z + 3z2) = 0 Solving 72 + 35z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + z)(8 + 3z) = 0Subproblem 1
Set the factor '(9 + z)' equal to zero and attempt to solve: Simplifying 9 + z = 0 Solving 9 + z = 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 + z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + z = 0 + -9 z = 0 + -9 Combine like terms: 0 + -9 = -9 z = -9 Simplifying z = -9Subproblem 2
Set the factor '(8 + 3z)' equal to zero and attempt to solve: Simplifying 8 + 3z = 0 Solving 8 + 3z = 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 + 3z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3z = 0 + -8 3z = 0 + -8 Combine like terms: 0 + -8 = -8 3z = -8 Divide each side by '3'. z = -2.666666667 Simplifying z = -2.666666667Solution
z = {-9, -2.666666667}
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