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Simplifying (4z + 6)(5 + -1z) = 0 Reorder the terms: (6 + 4z)(5 + -1z) = 0 Multiply (6 + 4z) * (5 + -1z) (6(5 + -1z) + 4z * (5 + -1z)) = 0 ((5 * 6 + -1z * 6) + 4z * (5 + -1z)) = 0 ((30 + -6z) + 4z * (5 + -1z)) = 0 (30 + -6z + (5 * 4z + -1z * 4z)) = 0 (30 + -6z + (20z + -4z2)) = 0 Combine like terms: -6z + 20z = 14z (30 + 14z + -4z2) = 0 Solving 30 + 14z + -4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 7z + -2z2) = 0 Factor a trinomial. 2((5 + -1z)(3 + 2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 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 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Subproblem 2
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 = -1.5Solution
z = {5, -1.5}
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