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Simplifying 6q2 + -7q = 5q2 + -9q + 48 Reorder the terms: -7q + 6q2 = 5q2 + -9q + 48 Reorder the terms: -7q + 6q2 = 48 + -9q + 5q2 Solving -7q + 6q2 = 48 + -9q + 5q2 Solving for variable 'q'. Reorder the terms: -48 + -7q + 9q + 6q2 + -5q2 = 48 + -9q + 5q2 + -48 + 9q + -5q2 Combine like terms: -7q + 9q = 2q -48 + 2q + 6q2 + -5q2 = 48 + -9q + 5q2 + -48 + 9q + -5q2 Combine like terms: 6q2 + -5q2 = 1q2 -48 + 2q + 1q2 = 48 + -9q + 5q2 + -48 + 9q + -5q2 Reorder the terms: -48 + 2q + 1q2 = 48 + -48 + -9q + 9q + 5q2 + -5q2 Combine like terms: 48 + -48 = 0 -48 + 2q + 1q2 = 0 + -9q + 9q + 5q2 + -5q2 -48 + 2q + 1q2 = -9q + 9q + 5q2 + -5q2 Combine like terms: -9q + 9q = 0 -48 + 2q + 1q2 = 0 + 5q2 + -5q2 -48 + 2q + 1q2 = 5q2 + -5q2 Combine like terms: 5q2 + -5q2 = 0 -48 + 2q + 1q2 = 0 Factor a trinomial. (-8 + -1q)(6 + -1q) = 0Subproblem 1
Set the factor '(-8 + -1q)' equal to zero and attempt to solve: Simplifying -8 + -1q = 0 Solving -8 + -1q = 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 + -1q = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1q = 0 + 8 -1q = 0 + 8 Combine like terms: 0 + 8 = 8 -1q = 8 Divide each side by '-1'. q = -8 Simplifying q = -8Subproblem 2
Set the factor '(6 + -1q)' equal to zero and attempt to solve: Simplifying 6 + -1q = 0 Solving 6 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1q = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1q = 0 + -6 -1q = 0 + -6 Combine like terms: 0 + -6 = -6 -1q = -6 Divide each side by '-1'. q = 6 Simplifying q = 6Solution
q = {-8, 6}
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