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Simplifying (6q + 7)(2q + 3) = 0 Reorder the terms: (7 + 6q)(2q + 3) = 0 Reorder the terms: (7 + 6q)(3 + 2q) = 0 Multiply (7 + 6q) * (3 + 2q) (7(3 + 2q) + 6q * (3 + 2q)) = 0 ((3 * 7 + 2q * 7) + 6q * (3 + 2q)) = 0 ((21 + 14q) + 6q * (3 + 2q)) = 0 (21 + 14q + (3 * 6q + 2q * 6q)) = 0 (21 + 14q + (18q + 12q2)) = 0 Combine like terms: 14q + 18q = 32q (21 + 32q + 12q2) = 0 Solving 21 + 32q + 12q2 = 0 Solving for variable 'q'. Factor a trinomial. (3 + 2q)(7 + 6q) = 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 + 6q)' equal to zero and attempt to solve: Simplifying 7 + 6q = 0 Solving 7 + 6q = 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 + 6q = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6q = 0 + -7 6q = 0 + -7 Combine like terms: 0 + -7 = -7 6q = -7 Divide each side by '6'. q = -1.166666667 Simplifying q = -1.166666667Solution
q = {-1.5, -1.166666667}
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