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Simplifying 6q2 + -3q = 5q2 + -8q + 24 Reorder the terms: -3q + 6q2 = 5q2 + -8q + 24 Reorder the terms: -3q + 6q2 = 24 + -8q + 5q2 Solving -3q + 6q2 = 24 + -8q + 5q2 Solving for variable 'q'. Reorder the terms: -24 + -3q + 8q + 6q2 + -5q2 = 24 + -8q + 5q2 + -24 + 8q + -5q2 Combine like terms: -3q + 8q = 5q -24 + 5q + 6q2 + -5q2 = 24 + -8q + 5q2 + -24 + 8q + -5q2 Combine like terms: 6q2 + -5q2 = 1q2 -24 + 5q + 1q2 = 24 + -8q + 5q2 + -24 + 8q + -5q2 Reorder the terms: -24 + 5q + 1q2 = 24 + -24 + -8q + 8q + 5q2 + -5q2 Combine like terms: 24 + -24 = 0 -24 + 5q + 1q2 = 0 + -8q + 8q + 5q2 + -5q2 -24 + 5q + 1q2 = -8q + 8q + 5q2 + -5q2 Combine like terms: -8q + 8q = 0 -24 + 5q + 1q2 = 0 + 5q2 + -5q2 -24 + 5q + 1q2 = 5q2 + -5q2 Combine like terms: 5q2 + -5q2 = 0 -24 + 5q + 1q2 = 0 Factor a trinomial. (-8 + -1q)(3 + -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 '(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 = {-8, 3}
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