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Simplifying (4z + 5)(2z + 3) = 0 Reorder the terms: (5 + 4z)(2z + 3) = 0 Reorder the terms: (5 + 4z)(3 + 2z) = 0 Multiply (5 + 4z) * (3 + 2z) (5(3 + 2z) + 4z * (3 + 2z)) = 0 ((3 * 5 + 2z * 5) + 4z * (3 + 2z)) = 0 ((15 + 10z) + 4z * (3 + 2z)) = 0 (15 + 10z + (3 * 4z + 2z * 4z)) = 0 (15 + 10z + (12z + 8z2)) = 0 Combine like terms: 10z + 12z = 22z (15 + 22z + 8z2) = 0 Solving 15 + 22z + 8z2 = 0 Solving for variable 'z'. Factor a trinomial. (3 + 2z)(5 + 4z) = 0Subproblem 1
Set the factor '(3 + 2z)' equal to zero and attempt to solve: Simplifying 3 + 2z = 0 Solving 3 + 2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2z = 0 + -3 2z = 0 + -3 Combine like terms: 0 + -3 = -3 2z = -3 Divide each side by '2'. z = -1.5 Simplifying z = -1.5Subproblem 2
Set the factor '(5 + 4z)' equal to zero and attempt to solve: Simplifying 5 + 4z = 0 Solving 5 + 4z = 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 + 4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4z = 0 + -5 4z = 0 + -5 Combine like terms: 0 + -5 = -5 4z = -5 Divide each side by '4'. z = -1.25 Simplifying z = -1.25Solution
z = {-1.5, -1.25}
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