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Simplifying (3z + 5)(9 + z) = 0 Reorder the terms: (5 + 3z)(9 + z) = 0 Multiply (5 + 3z) * (9 + z) (5(9 + z) + 3z * (9 + z)) = 0 ((9 * 5 + z * 5) + 3z * (9 + z)) = 0 ((45 + 5z) + 3z * (9 + z)) = 0 (45 + 5z + (9 * 3z + z * 3z)) = 0 (45 + 5z + (27z + 3z2)) = 0 Combine like terms: 5z + 27z = 32z (45 + 32z + 3z2) = 0 Solving 45 + 32z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + z)(5 + 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 '(5 + 3z)' equal to zero and attempt to solve: Simplifying 5 + 3z = 0 Solving 5 + 3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3z = 0 + -5 3z = 0 + -5 Combine like terms: 0 + -5 = -5 3z = -5 Divide each side by '3'. z = -1.666666667 Simplifying z = -1.666666667Solution
z = {-9, -1.666666667}
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