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Simplifying (3z + 8)(z + 5) = 0 Reorder the terms: (8 + 3z)(z + 5) = 0 Reorder the terms: (8 + 3z)(5 + z) = 0 Multiply (8 + 3z) * (5 + z) (8(5 + z) + 3z * (5 + z)) = 0 ((5 * 8 + z * 8) + 3z * (5 + z)) = 0 ((40 + 8z) + 3z * (5 + z)) = 0 (40 + 8z + (5 * 3z + z * 3z)) = 0 (40 + 8z + (15z + 3z2)) = 0 Combine like terms: 8z + 15z = 23z (40 + 23z + 3z2) = 0 Solving 40 + 23z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + z)(8 + 3z) = 0Subproblem 1
Set the factor '(5 + z)' equal to zero and attempt to solve: Simplifying 5 + z = 0 Solving 5 + z = 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 + z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z = 0 + -5 z = 0 + -5 Combine like terms: 0 + -5 = -5 z = -5 Simplifying z = -5Subproblem 2
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 = -2.666666667Solution
z = {-5, -2.666666667}
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