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Simplifying (4z + 2)(5 + -1z) = 0 Reorder the terms: (2 + 4z)(5 + -1z) = 0 Multiply (2 + 4z) * (5 + -1z) (2(5 + -1z) + 4z * (5 + -1z)) = 0 ((5 * 2 + -1z * 2) + 4z * (5 + -1z)) = 0 ((10 + -2z) + 4z * (5 + -1z)) = 0 (10 + -2z + (5 * 4z + -1z * 4z)) = 0 (10 + -2z + (20z + -4z2)) = 0 Combine like terms: -2z + 20z = 18z (10 + 18z + -4z2) = 0 Solving 10 + 18z + -4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 9z + -2z2) = 0 Factor a trinomial. 2((5 + -1z)(1 + 2z)) = 0 Ignore the factor 2.Subproblem 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 '(1 + 2z)' equal to zero and attempt to solve: Simplifying 1 + 2z = 0 Solving 1 + 2z = 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 + 2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2z = 0 + -1 2z = 0 + -1 Combine like terms: 0 + -1 = -1 2z = -1 Divide each side by '2'. z = -0.5 Simplifying z = -0.5Solution
z = {5, -0.5}
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