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Simplifying 7q + -21 = q2 + q + -12 Reorder the terms: -21 + 7q = q2 + q + -12 Reorder the terms: -21 + 7q = -12 + q + q2 Solving -21 + 7q = -12 + q + q2 Solving for variable 'q'. Reorder the terms: -21 + 12 + 7q + -1q + -1q2 = -12 + q + q2 + 12 + -1q + -1q2 Combine like terms: -21 + 12 = -9 -9 + 7q + -1q + -1q2 = -12 + q + q2 + 12 + -1q + -1q2 Combine like terms: 7q + -1q = 6q -9 + 6q + -1q2 = -12 + q + q2 + 12 + -1q + -1q2 Reorder the terms: -9 + 6q + -1q2 = -12 + 12 + q + -1q + q2 + -1q2 Combine like terms: -12 + 12 = 0 -9 + 6q + -1q2 = 0 + q + -1q + q2 + -1q2 -9 + 6q + -1q2 = q + -1q + q2 + -1q2 Combine like terms: q + -1q = 0 -9 + 6q + -1q2 = 0 + q2 + -1q2 -9 + 6q + -1q2 = q2 + -1q2 Combine like terms: q2 + -1q2 = 0 -9 + 6q + -1q2 = 0 Factor a trinomial. (-3 + q)(3 + -1q) = 0Subproblem 1
Set the factor '(-3 + q)' equal to zero and attempt to solve: Simplifying -3 + q = 0 Solving -3 + q = 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 + q = 0 + 3 Combine like terms: -3 + 3 = 0 0 + q = 0 + 3 q = 0 + 3 Combine like terms: 0 + 3 = 3 q = 3 Simplifying q = 3Subproblem 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 = {3, 3}
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