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Simplifying (8 + z)(3z + 5) = 0 Reorder the terms: (8 + z)(5 + 3z) = 0 Multiply (8 + z) * (5 + 3z) (8(5 + 3z) + z(5 + 3z)) = 0 ((5 * 8 + 3z * 8) + z(5 + 3z)) = 0 ((40 + 24z) + z(5 + 3z)) = 0 (40 + 24z + (5 * z + 3z * z)) = 0 (40 + 24z + (5z + 3z2)) = 0 Combine like terms: 24z + 5z = 29z (40 + 29z + 3z2) = 0 Solving 40 + 29z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (8 + z)(5 + 3z) = 0Subproblem 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 '(5 + 3z)' equal to zero and attempt to solve: Simplifying 5 + 3z = 0 Solving 5 + 3z = 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 + 3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3z = 0 + -5 3z = 0 + -5 Combine like terms: 0 + -5 = -5 3z = -5 Divide each side by '3'. z = -1.666666667 Simplifying z = -1.666666667Solution
z = {-8, -1.666666667}
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