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Simplifying (3z + 5)(2z + 7) = 0 Reorder the terms: (5 + 3z)(2z + 7) = 0 Reorder the terms: (5 + 3z)(7 + 2z) = 0 Multiply (5 + 3z) * (7 + 2z) (5(7 + 2z) + 3z * (7 + 2z)) = 0 ((7 * 5 + 2z * 5) + 3z * (7 + 2z)) = 0 ((35 + 10z) + 3z * (7 + 2z)) = 0 (35 + 10z + (7 * 3z + 2z * 3z)) = 0 (35 + 10z + (21z + 6z2)) = 0 Combine like terms: 10z + 21z = 31z (35 + 31z + 6z2) = 0 Solving 35 + 31z + 6z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + 2z)(5 + 3z) = 0Subproblem 1
Set the factor '(7 + 2z)' equal to zero and attempt to solve: Simplifying 7 + 2z = 0 Solving 7 + 2z = 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 + 2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2z = 0 + -7 2z = 0 + -7 Combine like terms: 0 + -7 = -7 2z = -7 Divide each side by '2'. z = -3.5 Simplifying z = -3.5Subproblem 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 = {-3.5, -1.666666667}
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