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Simplifying (9 + z)(3z + 2) = 0 Reorder the terms: (9 + z)(2 + 3z) = 0 Multiply (9 + z) * (2 + 3z) (9(2 + 3z) + z(2 + 3z)) = 0 ((2 * 9 + 3z * 9) + z(2 + 3z)) = 0 ((18 + 27z) + z(2 + 3z)) = 0 (18 + 27z + (2 * z + 3z * z)) = 0 (18 + 27z + (2z + 3z2)) = 0 Combine like terms: 27z + 2z = 29z (18 + 29z + 3z2) = 0 Solving 18 + 29z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (9 + z)(2 + 3z) = 0Subproblem 1
Set the factor '(9 + z)' equal to zero and attempt to solve: Simplifying 9 + z = 0 Solving 9 + z = 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 + z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + z = 0 + -9 z = 0 + -9 Combine like terms: 0 + -9 = -9 z = -9 Simplifying z = -9Subproblem 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 = {-9, -0.6666666667}
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