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Simplifying (4z + 5)(1 + -1z) = 0 Reorder the terms: (5 + 4z)(1 + -1z) = 0 Multiply (5 + 4z) * (1 + -1z) (5(1 + -1z) + 4z * (1 + -1z)) = 0 ((1 * 5 + -1z * 5) + 4z * (1 + -1z)) = 0 ((5 + -5z) + 4z * (1 + -1z)) = 0 (5 + -5z + (1 * 4z + -1z * 4z)) = 0 (5 + -5z + (4z + -4z2)) = 0 Combine like terms: -5z + 4z = -1z (5 + -1z + -4z2) = 0 Solving 5 + -1z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (1 + -1z)(5 + 4z) = 0Subproblem 1
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Subproblem 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 = {1, -1.25}
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