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Simplifying (4z + 2)(8 + z) = 0 Reorder the terms: (2 + 4z)(8 + z) = 0 Multiply (2 + 4z) * (8 + z) (2(8 + z) + 4z * (8 + z)) = 0 ((8 * 2 + z * 2) + 4z * (8 + z)) = 0 ((16 + 2z) + 4z * (8 + z)) = 0 (16 + 2z + (8 * 4z + z * 4z)) = 0 (16 + 2z + (32z + 4z2)) = 0 Combine like terms: 2z + 32z = 34z (16 + 34z + 4z2) = 0 Solving 16 + 34z + 4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 17z + 2z2) = 0 Factor a trinomial. 2((8 + z)(1 + 2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + z)' equal to zero and attempt to solve: Simplifying 8 + z = 0 Solving 8 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + z = 0 + -8 z = 0 + -8 Combine like terms: 0 + -8 = -8 z = -8 Simplifying z = -8Subproblem 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 = {-8, -0.5}
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