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Simplifying (9 + z)(3z + 4) = 0 Reorder the terms: (9 + z)(4 + 3z) = 0 Multiply (9 + z) * (4 + 3z) (9(4 + 3z) + z(4 + 3z)) = 0 ((4 * 9 + 3z * 9) + z(4 + 3z)) = 0 ((36 + 27z) + z(4 + 3z)) = 0 (36 + 27z + (4 * z + 3z * z)) = 0 (36 + 27z + (4z + 3z2)) = 0 Combine like terms: 27z + 4z = 31z (36 + 31z + 3z2) = 0 Solving 36 + 31z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + z)(4 + 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 '(4 + 3z)' equal to zero and attempt to solve: Simplifying 4 + 3z = 0 Solving 4 + 3z = 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 + 3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3z = 0 + -4 3z = 0 + -4 Combine like terms: 0 + -4 = -4 3z = -4 Divide each side by '3'. z = -1.333333333 Simplifying z = -1.333333333Solution
z = {-9, -1.333333333}
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