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Simplifying (7q + 2)(3q + 8) = 0 Reorder the terms: (2 + 7q)(3q + 8) = 0 Reorder the terms: (2 + 7q)(8 + 3q) = 0 Multiply (2 + 7q) * (8 + 3q) (2(8 + 3q) + 7q * (8 + 3q)) = 0 ((8 * 2 + 3q * 2) + 7q * (8 + 3q)) = 0 ((16 + 6q) + 7q * (8 + 3q)) = 0 (16 + 6q + (8 * 7q + 3q * 7q)) = 0 (16 + 6q + (56q + 21q2)) = 0 Combine like terms: 6q + 56q = 62q (16 + 62q + 21q2) = 0 Solving 16 + 62q + 21q2 = 0 Solving for variable 'q'. Factor a trinomial. (8 + 3q)(2 + 7q) = 0Subproblem 1
Set the factor '(8 + 3q)' equal to zero and attempt to solve: Simplifying 8 + 3q = 0 Solving 8 + 3q = 0 Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3q = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3q = 0 + -8 3q = 0 + -8 Combine like terms: 0 + -8 = -8 3q = -8 Divide each side by '3'. q = -2.666666667 Simplifying q = -2.666666667Subproblem 2
Set the factor '(2 + 7q)' equal to zero and attempt to solve: Simplifying 2 + 7q = 0 Solving 2 + 7q = 0 Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 7q = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7q = 0 + -2 7q = 0 + -2 Combine like terms: 0 + -2 = -2 7q = -2 Divide each side by '7'. q = -0.2857142857 Simplifying q = -0.2857142857Solution
q = {-2.666666667, -0.2857142857}
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