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Simplifying (3z + 6)(2z + 7) = 0 Reorder the terms: (6 + 3z)(2z + 7) = 0 Reorder the terms: (6 + 3z)(7 + 2z) = 0 Multiply (6 + 3z) * (7 + 2z) (6(7 + 2z) + 3z * (7 + 2z)) = 0 ((7 * 6 + 2z * 6) + 3z * (7 + 2z)) = 0 ((42 + 12z) + 3z * (7 + 2z)) = 0 (42 + 12z + (7 * 3z + 2z * 3z)) = 0 (42 + 12z + (21z + 6z2)) = 0 Combine like terms: 12z + 21z = 33z (42 + 33z + 6z2) = 0 Solving 42 + 33z + 6z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + 11z + 2z2) = 0 Factor a trinomial. 3((7 + 2z)(2 + z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + 2z)' equal to zero and attempt to solve: Simplifying 7 + 2z = 0 Solving 7 + 2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2z = 0 + -7 2z = 0 + -7 Combine like terms: 0 + -7 = -7 2z = -7 Divide each side by '2'. z = -3.5 Simplifying z = -3.5Subproblem 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 = {-3.5, -2}
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