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Simplifying (3z + 2)(6 + z) = 0 Reorder the terms: (2 + 3z)(6 + z) = 0 Multiply (2 + 3z) * (6 + z) (2(6 + z) + 3z * (6 + z)) = 0 ((6 * 2 + z * 2) + 3z * (6 + z)) = 0 ((12 + 2z) + 3z * (6 + z)) = 0 (12 + 2z + (6 * 3z + z * 3z)) = 0 (12 + 2z + (18z + 3z2)) = 0 Combine like terms: 2z + 18z = 20z (12 + 20z + 3z2) = 0 Solving 12 + 20z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (6 + z)(2 + 3z) = 0Subproblem 1
Set the factor '(6 + z)' equal to zero and attempt to solve: Simplifying 6 + z = 0 Solving 6 + z = 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 + z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + z = 0 + -6 z = 0 + -6 Combine like terms: 0 + -6 = -6 z = -6 Simplifying z = -6Subproblem 2
Set the factor '(2 + 3z)' equal to zero and attempt to solve: Simplifying 2 + 3z = 0 Solving 2 + 3z = 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 + 3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3z = 0 + -2 3z = 0 + -2 Combine like terms: 0 + -2 = -2 3z = -2 Divide each side by '3'. z = -0.6666666667 Simplifying z = -0.6666666667Solution
z = {-6, -0.6666666667}
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