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Simplifying (5z + 8)(1 + -1z) = 0 Reorder the terms: (8 + 5z)(1 + -1z) = 0 Multiply (8 + 5z) * (1 + -1z) (8(1 + -1z) + 5z * (1 + -1z)) = 0 ((1 * 8 + -1z * 8) + 5z * (1 + -1z)) = 0 ((8 + -8z) + 5z * (1 + -1z)) = 0 (8 + -8z + (1 * 5z + -1z * 5z)) = 0 (8 + -8z + (5z + -5z2)) = 0 Combine like terms: -8z + 5z = -3z (8 + -3z + -5z2) = 0 Solving 8 + -3z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (1 + -1z)(8 + 5z) = 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 '(8 + 5z)' equal to zero and attempt to solve: Simplifying 8 + 5z = 0 Solving 8 + 5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 5z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5z = 0 + -8 5z = 0 + -8 Combine like terms: 0 + -8 = -8 5z = -8 Divide each side by '5'. z = -1.6 Simplifying z = -1.6Solution
z = {1, -1.6}
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