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Simplifying (3 + -1z)(4z + 5) = 0 Reorder the terms: (3 + -1z)(5 + 4z) = 0 Multiply (3 + -1z) * (5 + 4z) (3(5 + 4z) + -1z * (5 + 4z)) = 0 ((5 * 3 + 4z * 3) + -1z * (5 + 4z)) = 0 ((15 + 12z) + -1z * (5 + 4z)) = 0 (15 + 12z + (5 * -1z + 4z * -1z)) = 0 (15 + 12z + (-5z + -4z2)) = 0 Combine like terms: 12z + -5z = 7z (15 + 7z + -4z2) = 0 Solving 15 + 7z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (3 + -1z)(5 + 4z) = 0Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Subproblem 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 = {3, -1.25}
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