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Simplifying (6q2) + -3q = (5q2) + -7q + 12 Reorder the terms: -3q + (6q2) = (5q2) + -7q + 12 Reorder the terms: -3q + (6q2) = 12 + -7q + (5q2) Solving -3q + (6q2) = 12 + -7q + (5q2) Solving for variable 'q'. Reorder the terms: -12 + -3q + 7q + (6q2) + (-5q2) = 12 + -7q + (5q2) + -12 + 7q + (-5q2) Combine like terms: -3q + 7q = 4q -12 + 4q + (6q2) + (-5q2) = 12 + -7q + (5q2) + -12 + 7q + (-5q2) Combine like terms: (6q2) + (-5q2) = 1q2 -12 + 4q + 1q2 = 12 + -7q + (5q2) + -12 + 7q + (-5q2) Reorder the terms: -12 + 4q + 1q2 = 12 + -12 + -7q + 7q + (5q2) + (-5q2) Combine like terms: 12 + -12 = 0 -12 + 4q + 1q2 = 0 + -7q + 7q + (5q2) + (-5q2) -12 + 4q + 1q2 = -7q + 7q + (5q2) + (-5q2) Combine like terms: -7q + 7q = 0 -12 + 4q + 1q2 = 0 + (5q2) + (-5q2) -12 + 4q + 1q2 = (5q2) + (-5q2) Combine like terms: (5q2) + (-5q2) = 0 -12 + 4q + 1q2 = 0 Factor a trinomial. (-6 + -1q)(2 + -1q) = 0Subproblem 1
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 = -6Subproblem 2
Set the factor '(2 + -1q)' equal to zero and attempt to solve: Simplifying 2 + -1q = 0 Solving 2 + -1q = 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 + -1q = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1q = 0 + -2 -1q = 0 + -2 Combine like terms: 0 + -2 = -2 -1q = -2 Divide each side by '-1'. q = 2 Simplifying q = 2Solution
q = {-6, 2}
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