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Simplifying (4z + 5)(4 + z) = 0 Reorder the terms: (5 + 4z)(4 + z) = 0 Multiply (5 + 4z) * (4 + z) (5(4 + z) + 4z * (4 + z)) = 0 ((4 * 5 + z * 5) + 4z * (4 + z)) = 0 ((20 + 5z) + 4z * (4 + z)) = 0 (20 + 5z + (4 * 4z + z * 4z)) = 0 (20 + 5z + (16z + 4z2)) = 0 Combine like terms: 5z + 16z = 21z (20 + 21z + 4z2) = 0 Solving 20 + 21z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + z)(5 + 4z) = 0Subproblem 1
Set the factor '(4 + z)' equal to zero and attempt to solve: Simplifying 4 + z = 0 Solving 4 + z = 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 + z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z = 0 + -4 z = 0 + -4 Combine like terms: 0 + -4 = -4 z = -4 Simplifying z = -4Subproblem 2
Set the factor '(5 + 4z)' equal to zero and attempt to solve: Simplifying 5 + 4z = 0 Solving 5 + 4z = 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 + 4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4z = 0 + -5 4z = 0 + -5 Combine like terms: 0 + -5 = -5 4z = -5 Divide each side by '4'. z = -1.25 Simplifying z = -1.25Solution
z = {-4, -1.25}
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