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Simplifying (8z + 2)(5z + 8) = 0 Reorder the terms: (2 + 8z)(5z + 8) = 0 Reorder the terms: (2 + 8z)(8 + 5z) = 0 Multiply (2 + 8z) * (8 + 5z) (2(8 + 5z) + 8z * (8 + 5z)) = 0 ((8 * 2 + 5z * 2) + 8z * (8 + 5z)) = 0 ((16 + 10z) + 8z * (8 + 5z)) = 0 (16 + 10z + (8 * 8z + 5z * 8z)) = 0 (16 + 10z + (64z + 40z2)) = 0 Combine like terms: 10z + 64z = 74z (16 + 74z + 40z2) = 0 Solving 16 + 74z + 40z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 37z + 20z2) = 0 Factor a trinomial. 2((8 + 5z)(1 + 4z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + 5z)' equal to zero and attempt to solve: Simplifying 8 + 5z = 0 Solving 8 + 5z = 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 + 5z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5z = 0 + -8 5z = 0 + -8 Combine like terms: 0 + -8 = -8 5z = -8 Divide each side by '5'. z = -1.6 Simplifying z = -1.6Subproblem 2
Set the factor '(1 + 4z)' equal to zero and attempt to solve: Simplifying 1 + 4z = 0 Solving 1 + 4z = 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 + 4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4z = 0 + -1 4z = 0 + -1 Combine like terms: 0 + -1 = -1 4z = -1 Divide each side by '4'. z = -0.25 Simplifying z = -0.25Solution
z = {-1.6, -0.25}
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