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Simplifying (5z + 4)(5 + -1z) = 0 Reorder the terms: (4 + 5z)(5 + -1z) = 0 Multiply (4 + 5z) * (5 + -1z) (4(5 + -1z) + 5z * (5 + -1z)) = 0 ((5 * 4 + -1z * 4) + 5z * (5 + -1z)) = 0 ((20 + -4z) + 5z * (5 + -1z)) = 0 (20 + -4z + (5 * 5z + -1z * 5z)) = 0 (20 + -4z + (25z + -5z2)) = 0 Combine like terms: -4z + 25z = 21z (20 + 21z + -5z2) = 0 Solving 20 + 21z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + -1z)(4 + 5z) = 0Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 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 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Subproblem 2
Set the factor '(4 + 5z)' equal to zero and attempt to solve: Simplifying 4 + 5z = 0 Solving 4 + 5z = 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 + 5z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5z = 0 + -4 5z = 0 + -4 Combine like terms: 0 + -4 = -4 5z = -4 Divide each side by '5'. z = -0.8 Simplifying z = -0.8Solution
z = {5, -0.8}
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