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Simplifying 8q3 + 6q2 + -9q = 0 Reorder the terms: -9q + 6q2 + 8q3 = 0 Solving -9q + 6q2 + 8q3 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), 'q'. q(-9 + 6q + 8q2) = 0 Factor a trinomial. q((-3 + -2q)(3 + -4q)) = 0Subproblem 1
Set the factor 'q' equal to zero and attempt to solve: Simplifying q = 0 Solving q = 0 Move all terms containing q to the left, all other terms to the right. Simplifying q = 0Subproblem 2
Set the factor '(-3 + -2q)' equal to zero and attempt to solve: Simplifying -3 + -2q = 0 Solving -3 + -2q = 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 + -2q = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2q = 0 + 3 -2q = 0 + 3 Combine like terms: 0 + 3 = 3 -2q = 3 Divide each side by '-2'. q = -1.5 Simplifying q = -1.5Subproblem 3
Set the factor '(3 + -4q)' equal to zero and attempt to solve: Simplifying 3 + -4q = 0 Solving 3 + -4q = 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 + -4q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4q = 0 + -3 -4q = 0 + -3 Combine like terms: 0 + -3 = -3 -4q = -3 Divide each side by '-4'. q = 0.75 Simplifying q = 0.75Solution
q = {0, -1.5, 0.75}
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