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Simplifying (12q + 7)(2q + 3) = 0 Reorder the terms: (7 + 12q)(2q + 3) = 0 Reorder the terms: (7 + 12q)(3 + 2q) = 0 Multiply (7 + 12q) * (3 + 2q) (7(3 + 2q) + 12q * (3 + 2q)) = 0 ((3 * 7 + 2q * 7) + 12q * (3 + 2q)) = 0 ((21 + 14q) + 12q * (3 + 2q)) = 0 (21 + 14q + (3 * 12q + 2q * 12q)) = 0 (21 + 14q + (36q + 24q2)) = 0 Combine like terms: 14q + 36q = 50q (21 + 50q + 24q2) = 0 Solving 21 + 50q + 24q2 = 0 Solving for variable 'q'. Factor a trinomial. (3 + 2q)(7 + 12q) = 0Subproblem 1
Set the factor '(3 + 2q)' equal to zero and attempt to solve: Simplifying 3 + 2q = 0 Solving 3 + 2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2q = 0 + -3 2q = 0 + -3 Combine like terms: 0 + -3 = -3 2q = -3 Divide each side by '2'. q = -1.5 Simplifying q = -1.5Subproblem 2
Set the factor '(7 + 12q)' equal to zero and attempt to solve: Simplifying 7 + 12q = 0 Solving 7 + 12q = 0 Move all terms containing q to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 12q = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 12q = 0 + -7 12q = 0 + -7 Combine like terms: 0 + -7 = -7 12q = -7 Divide each side by '12'. q = -0.5833333333 Simplifying q = -0.5833333333Solution
q = {-1.5, -0.5833333333}
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