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Simplifying (2z + 5)(6 + -1z) = 0 Reorder the terms: (5 + 2z)(6 + -1z) = 0 Multiply (5 + 2z) * (6 + -1z) (5(6 + -1z) + 2z * (6 + -1z)) = 0 ((6 * 5 + -1z * 5) + 2z * (6 + -1z)) = 0 ((30 + -5z) + 2z * (6 + -1z)) = 0 (30 + -5z + (6 * 2z + -1z * 2z)) = 0 (30 + -5z + (12z + -2z2)) = 0 Combine like terms: -5z + 12z = 7z (30 + 7z + -2z2) = 0 Solving 30 + 7z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (6 + -1z)(5 + 2z) = 0Subproblem 1
Set the factor '(6 + -1z)' equal to zero and attempt to solve: Simplifying 6 + -1z = 0 Solving 6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1z = 0 + -6 -1z = 0 + -6 Combine like terms: 0 + -6 = -6 -1z = -6 Divide each side by '-1'. z = 6 Simplifying z = 6Subproblem 2
Set the factor '(5 + 2z)' equal to zero and attempt to solve: Simplifying 5 + 2z = 0 Solving 5 + 2z = 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 + 2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2z = 0 + -5 2z = 0 + -5 Combine like terms: 0 + -5 = -5 2z = -5 Divide each side by '2'. z = -2.5 Simplifying z = -2.5Solution
z = {6, -2.5}
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