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Simplifying (8z + 5)(6z + 9) = 0 Reorder the terms: (5 + 8z)(6z + 9) = 0 Reorder the terms: (5 + 8z)(9 + 6z) = 0 Multiply (5 + 8z) * (9 + 6z) (5(9 + 6z) + 8z * (9 + 6z)) = 0 ((9 * 5 + 6z * 5) + 8z * (9 + 6z)) = 0 ((45 + 30z) + 8z * (9 + 6z)) = 0 (45 + 30z + (9 * 8z + 6z * 8z)) = 0 (45 + 30z + (72z + 48z2)) = 0 Combine like terms: 30z + 72z = 102z (45 + 102z + 48z2) = 0 Solving 45 + 102z + 48z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3'. 3(15 + 34z + 16z2) = 0 Factor a trinomial. 3((3 + 2z)(5 + 8z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 2z)' equal to zero and attempt to solve: Simplifying 3 + 2z = 0 Solving 3 + 2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2z = 0 + -3 2z = 0 + -3 Combine like terms: 0 + -3 = -3 2z = -3 Divide each side by '2'. z = -1.5 Simplifying z = -1.5Subproblem 2
Set the factor '(5 + 8z)' equal to zero and attempt to solve: Simplifying 5 + 8z = 0 Solving 5 + 8z = 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 + 8z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8z = 0 + -5 8z = 0 + -5 Combine like terms: 0 + -5 = -5 8z = -5 Divide each side by '8'. z = -0.625 Simplifying z = -0.625Solution
z = {-1.5, -0.625}
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