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Simplifying (4 + -1z)(4z + 2) = 0 Reorder the terms: (4 + -1z)(2 + 4z) = 0 Multiply (4 + -1z) * (2 + 4z) (4(2 + 4z) + -1z * (2 + 4z)) = 0 ((2 * 4 + 4z * 4) + -1z * (2 + 4z)) = 0 ((8 + 16z) + -1z * (2 + 4z)) = 0 (8 + 16z + (2 * -1z + 4z * -1z)) = 0 (8 + 16z + (-2z + -4z2)) = 0 Combine like terms: 16z + -2z = 14z (8 + 14z + -4z2) = 0 Solving 8 + 14z + -4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 7z + -2z2) = 0 Factor a trinomial. 2((4 + -1z)(1 + 2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 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 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Subproblem 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 = {4, -0.5}
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