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Simplifying (5 + z)(4z + 9) = 0 Reorder the terms: (5 + z)(9 + 4z) = 0 Multiply (5 + z) * (9 + 4z) (5(9 + 4z) + z(9 + 4z)) = 0 ((9 * 5 + 4z * 5) + z(9 + 4z)) = 0 ((45 + 20z) + z(9 + 4z)) = 0 (45 + 20z + (9 * z + 4z * z)) = 0 (45 + 20z + (9z + 4z2)) = 0 Combine like terms: 20z + 9z = 29z (45 + 29z + 4z2) = 0 Solving 45 + 29z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + z)(9 + 4z) = 0Subproblem 1
Set the factor '(5 + z)' equal to zero and attempt to solve: Simplifying 5 + z = 0 Solving 5 + z = 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 + z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z = 0 + -5 z = 0 + -5 Combine like terms: 0 + -5 = -5 z = -5 Simplifying z = -5Subproblem 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 = {-5, -2.25}
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