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Simplifying (6z + 12)(2z + 9) = 0 Reorder the terms: (12 + 6z)(2z + 9) = 0 Reorder the terms: (12 + 6z)(9 + 2z) = 0 Multiply (12 + 6z) * (9 + 2z) (12(9 + 2z) + 6z * (9 + 2z)) = 0 ((9 * 12 + 2z * 12) + 6z * (9 + 2z)) = 0 ((108 + 24z) + 6z * (9 + 2z)) = 0 (108 + 24z + (9 * 6z + 2z * 6z)) = 0 (108 + 24z + (54z + 12z2)) = 0 Combine like terms: 24z + 54z = 78z (108 + 78z + 12z2) = 0 Solving 108 + 78z + 12z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '6'. 6(18 + 13z + 2z2) = 0 Factor a trinomial. 6((9 + 2z)(2 + z)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(9 + 2z)' equal to zero and attempt to solve: Simplifying 9 + 2z = 0 Solving 9 + 2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2z = 0 + -9 2z = 0 + -9 Combine like terms: 0 + -9 = -9 2z = -9 Divide each side by '2'. z = -4.5 Simplifying z = -4.5Subproblem 2
Set the factor '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Solution
z = {-4.5, -2}
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