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Simplifying 9q2 + -21q + 12 = 0 Reorder the terms: 12 + -21q + 9q2 = 0 Solving 12 + -21q + 9q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -7q + 3q2) = 0 Factor a trinomial. 3((1 + -1q)(4 + -3q)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -1q)' equal to zero and attempt to solve: Simplifying 1 + -1q = 0 Solving 1 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1q = 0 + -1 -1q = 0 + -1 Combine like terms: 0 + -1 = -1 -1q = -1 Divide each side by '-1'. q = 1 Simplifying q = 1Subproblem 2
Set the factor '(4 + -3q)' equal to zero and attempt to solve: Simplifying 4 + -3q = 0 Solving 4 + -3q = 0 Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3q = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3q = 0 + -4 -3q = 0 + -4 Combine like terms: 0 + -4 = -4 -3q = -4 Divide each side by '-3'. q = 1.333333333 Simplifying q = 1.333333333Solution
q = {1, 1.333333333}
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