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Simplifying (12q + 7)(2q + 5) = 0 Reorder the terms: (7 + 12q)(2q + 5) = 0 Reorder the terms: (7 + 12q)(5 + 2q) = 0 Multiply (7 + 12q) * (5 + 2q) (7(5 + 2q) + 12q * (5 + 2q)) = 0 ((5 * 7 + 2q * 7) + 12q * (5 + 2q)) = 0 ((35 + 14q) + 12q * (5 + 2q)) = 0 (35 + 14q + (5 * 12q + 2q * 12q)) = 0 (35 + 14q + (60q + 24q2)) = 0 Combine like terms: 14q + 60q = 74q (35 + 74q + 24q2) = 0 Solving 35 + 74q + 24q2 = 0 Solving for variable 'q'. Factor a trinomial. (5 + 2q)(7 + 12q) = 0Subproblem 1
Set the factor '(5 + 2q)' equal to zero and attempt to solve: Simplifying 5 + 2q = 0 Solving 5 + 2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2q = 0 + -5 2q = 0 + -5 Combine like terms: 0 + -5 = -5 2q = -5 Divide each side by '2'. q = -2.5 Simplifying q = -2.5Subproblem 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 = {-2.5, -0.5833333333}
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