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Simplifying (3z + 7)(5 + z) = 0 Reorder the terms: (7 + 3z)(5 + z) = 0 Multiply (7 + 3z) * (5 + z) (7(5 + z) + 3z * (5 + z)) = 0 ((5 * 7 + z * 7) + 3z * (5 + z)) = 0 ((35 + 7z) + 3z * (5 + z)) = 0 (35 + 7z + (5 * 3z + z * 3z)) = 0 (35 + 7z + (15z + 3z2)) = 0 Combine like terms: 7z + 15z = 22z (35 + 22z + 3z2) = 0 Solving 35 + 22z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + z)(7 + 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 '(7 + 3z)' equal to zero and attempt to solve: Simplifying 7 + 3z = 0 Solving 7 + 3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3z = 0 + -7 3z = 0 + -7 Combine like terms: 0 + -7 = -7 3z = -7 Divide each side by '3'. z = -2.333333333 Simplifying z = -2.333333333Solution
z = {-5, -2.333333333}
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