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Simplifying (4z + 2)(3z + 9) = 0 Reorder the terms: (2 + 4z)(3z + 9) = 0 Reorder the terms: (2 + 4z)(9 + 3z) = 0 Multiply (2 + 4z) * (9 + 3z) (2(9 + 3z) + 4z * (9 + 3z)) = 0 ((9 * 2 + 3z * 2) + 4z * (9 + 3z)) = 0 ((18 + 6z) + 4z * (9 + 3z)) = 0 (18 + 6z + (9 * 4z + 3z * 4z)) = 0 (18 + 6z + (36z + 12z2)) = 0 Combine like terms: 6z + 36z = 42z (18 + 42z + 12z2) = 0 Solving 18 + 42z + 12z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '6'. 6(3 + 7z + 2z2) = 0 Factor a trinomial. 6((3 + z)(1 + 2z)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + z)' equal to zero and attempt to solve: Simplifying 3 + z = 0 Solving 3 + z = 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 + z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + z = 0 + -3 z = 0 + -3 Combine like terms: 0 + -3 = -3 z = -3 Simplifying z = -3Subproblem 2
Set the factor '(1 + 2z)' equal to zero and attempt to solve: Simplifying 1 + 2z = 0 Solving 1 + 2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2z = 0 + -1 2z = 0 + -1 Combine like terms: 0 + -1 = -1 2z = -1 Divide each side by '2'. z = -0.5 Simplifying z = -0.5Solution
z = {-3, -0.5}
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