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Simplifying (3z + 8)(2 + z) = 0 Reorder the terms: (8 + 3z)(2 + z) = 0 Multiply (8 + 3z) * (2 + z) (8(2 + z) + 3z * (2 + z)) = 0 ((2 * 8 + z * 8) + 3z * (2 + z)) = 0 ((16 + 8z) + 3z * (2 + z)) = 0 (16 + 8z + (2 * 3z + z * 3z)) = 0 (16 + 8z + (6z + 3z2)) = 0 Combine like terms: 8z + 6z = 14z (16 + 14z + 3z2) = 0 Solving 16 + 14z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (8 + 3z)(2 + z) = 0Subproblem 1
Set the factor '(8 + 3z)' equal to zero and attempt to solve: Simplifying 8 + 3z = 0 Solving 8 + 3z = 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 + 3z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3z = 0 + -8 3z = 0 + -8 Combine like terms: 0 + -8 = -8 3z = -8 Divide each side by '3'. z = -2.666666667 Simplifying z = -2.666666667Subproblem 2
Set the factor '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Solution
z = {-2.666666667, -2}
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