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Simplifying (3z + 1)(8 + z) = 0 Reorder the terms: (1 + 3z)(8 + z) = 0 Multiply (1 + 3z) * (8 + z) (1(8 + z) + 3z * (8 + z)) = 0 ((8 * 1 + z * 1) + 3z * (8 + z)) = 0 ((8 + 1z) + 3z * (8 + z)) = 0 (8 + 1z + (8 * 3z + z * 3z)) = 0 (8 + 1z + (24z + 3z2)) = 0 Combine like terms: 1z + 24z = 25z (8 + 25z + 3z2) = 0 Solving 8 + 25z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (8 + z)(1 + 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 '(1 + 3z)' equal to zero and attempt to solve: Simplifying 1 + 3z = 0 Solving 1 + 3z = 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 + 3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3z = 0 + -1 3z = 0 + -1 Combine like terms: 0 + -1 = -1 3z = -1 Divide each side by '3'. z = -0.3333333333 Simplifying z = -0.3333333333Solution
z = {-8, -0.3333333333}
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