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Simplifying (3A + 2)(2A + 9) = 0 Reorder the terms: (2 + 3A)(2A + 9) = 0 Reorder the terms: (2 + 3A)(9 + 2A) = 0 Multiply (2 + 3A) * (9 + 2A) (2(9 + 2A) + 3A * (9 + 2A)) = 0 ((9 * 2 + 2A * 2) + 3A * (9 + 2A)) = 0 ((18 + 4A) + 3A * (9 + 2A)) = 0 (18 + 4A + (9 * 3A + 2A * 3A)) = 0 (18 + 4A + (27A + 6A2)) = 0 Combine like terms: 4A + 27A = 31A (18 + 31A + 6A2) = 0 Solving 18 + 31A + 6A2 = 0 Solving for variable 'A'. Factor a trinomial. (9 + 2A)(2 + 3A) = 0Subproblem 1
Set the factor '(9 + 2A)' equal to zero and attempt to solve: Simplifying 9 + 2A = 0 Solving 9 + 2A = 0 Move all terms containing A to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2A = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2A = 0 + -9 2A = 0 + -9 Combine like terms: 0 + -9 = -9 2A = -9 Divide each side by '2'. A = -4.5 Simplifying A = -4.5Subproblem 2
Set the factor '(2 + 3A)' equal to zero and attempt to solve: Simplifying 2 + 3A = 0 Solving 2 + 3A = 0 Move all terms containing A to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3A = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3A = 0 + -2 3A = 0 + -2 Combine like terms: 0 + -2 = -2 3A = -2 Divide each side by '3'. A = -0.6666666667 Simplifying A = -0.6666666667Solution
A = {-4.5, -0.6666666667}
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