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Simplifying 6q2 + 2q = 5q2 + -4q + 27 Reorder the terms: 2q + 6q2 = 5q2 + -4q + 27 Reorder the terms: 2q + 6q2 = 27 + -4q + 5q2 Solving 2q + 6q2 = 27 + -4q + 5q2 Solving for variable 'q'. Reorder the terms: -27 + 2q + 4q + 6q2 + -5q2 = 27 + -4q + 5q2 + -27 + 4q + -5q2 Combine like terms: 2q + 4q = 6q -27 + 6q + 6q2 + -5q2 = 27 + -4q + 5q2 + -27 + 4q + -5q2 Combine like terms: 6q2 + -5q2 = 1q2 -27 + 6q + 1q2 = 27 + -4q + 5q2 + -27 + 4q + -5q2 Reorder the terms: -27 + 6q + 1q2 = 27 + -27 + -4q + 4q + 5q2 + -5q2 Combine like terms: 27 + -27 = 0 -27 + 6q + 1q2 = 0 + -4q + 4q + 5q2 + -5q2 -27 + 6q + 1q2 = -4q + 4q + 5q2 + -5q2 Combine like terms: -4q + 4q = 0 -27 + 6q + 1q2 = 0 + 5q2 + -5q2 -27 + 6q + 1q2 = 5q2 + -5q2 Combine like terms: 5q2 + -5q2 = 0 -27 + 6q + 1q2 = 0 Factor a trinomial. (-9 + -1q)(3 + -1q) = 0Subproblem 1
Set the factor '(-9 + -1q)' equal to zero and attempt to solve: Simplifying -9 + -1q = 0 Solving -9 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1q = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1q = 0 + 9 -1q = 0 + 9 Combine like terms: 0 + 9 = 9 -1q = 9 Divide each side by '-1'. q = -9 Simplifying q = -9Subproblem 2
Set the factor '(3 + -1q)' equal to zero and attempt to solve: Simplifying 3 + -1q = 0 Solving 3 + -1q = 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 + -1q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1q = 0 + -3 -1q = 0 + -3 Combine like terms: 0 + -3 = -3 -1q = -3 Divide each side by '-1'. q = 3 Simplifying q = 3Solution
q = {-9, 3}
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