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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 = 9z (-5 + 9z + -4z2) = 0 Solving -5 + 9z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + 4z)(1 + -1z) = 0Subproblem 1
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 = 1.25Subproblem 2
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 = 1Solution
z = {1.25, 1}
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